image

    Have a query? Ask a Tutor!!

    Access to best educators and exclusive paper discussions

    Offsite CampusTurito Championship

    Can’t find what you’re looking for?

    Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

    • Homework- One to One Solutions
    • Understand concepts to solve better
    • Get your doubts solved instantly
    Maths-
    General
    Easy

    Question

    If fraction numerator x to the power of 2 end exponent minus 10 x plus 13 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent minus 5 x plus 6 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x minus 2 end fraction plus fraction numerator K over denominator x minus 3 end fraction then K=

    1. -1    
    2. -2    
    3. -3    
    4. -4    

    hintHint:

    • Take LCM on RHS and simplify
    • Then take a value of x which satisfies the requirement.

    The correct answer is: -4

       Given :
      fraction numerator x to the power of 2 end exponent minus 10 x plus 13 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent minus 5 x plus 6 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x minus 2 end fraction plus fraction numerator K over denominator x minus 3 end fraction

      Taking LCM on RHS and factorizing on LHS
      rightwards double arrow fraction numerator x squared minus 10 x plus 13 over denominator left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end fraction equals fraction numerator A left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis space plus space B left parenthesis x minus 1 right parenthesis left parenthesis x minus 3 right parenthesis space plus space K left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end fraction rightwards double arrow x squared minus 10 x plus 13 space equals space A left parenthesis x squared space minus 5 x space plus 6 right parenthesis plus space B left parenthesis x squared minus 4 x space plus 3 right parenthesis space plus space K left parenthesis x squared space minus 3 x space plus 2 right parenthesis rightwards double arrow x squared minus 10 x plus 13 space equals space A left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis space plus space B left parenthesis x minus 1 right parenthesis left parenthesis x minus 3 right parenthesis space plus space K left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis P u t space x equals space 3 rightwards double arrow 9 minus 30 plus 13 space equals space 0 plus 0 right parenthesis space plus space 2 K rightwards double arrow 2 K space equals space minus 8 rightwards double arrow space K space equals space minus 4
       

      Related Questions to study

      General
      Maths-

      If the remainders of the polynomial f left parenthesis x right parenthesis when divided by x plus 1 and x minus 1 are 7,3 then the remainder of f left parenthesis x right parenthesis when devided by x to the power of 2 end exponent minus 1 is

      If the remainders of the polynomial f left parenthesis x right parenthesis when divided by x plus 1 and x minus 1 are 7,3 then the remainder of f left parenthesis x right parenthesis when devided by x to the power of 2 end exponent minus 1 is

      Maths-General
      General
      Maths-

      If fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis left parenthesis c x plus d right parenthesis end fraction equals fraction numerator A over denominator a x plus b end fraction plus fraction numerator B over denominator c x plus d end fraction then fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis to the power of 2 end exponent left parenthesis c x plus d right parenthesis end fraction equals

      If fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis left parenthesis c x plus d right parenthesis end fraction equals fraction numerator A over denominator a x plus b end fraction plus fraction numerator B over denominator c x plus d end fraction then fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis to the power of 2 end exponent left parenthesis c x plus d right parenthesis end fraction equals

      Maths-General
      General
      Maths-

      The partial fractions of fraction numerator left parenthesis x plus 1 right parenthesis to the power of 2 end exponent over denominator x open parentheses x to the power of 2 end exponent plus 1 close parentheses end fraction are

      The partial fractions of fraction numerator left parenthesis x plus 1 right parenthesis to the power of 2 end exponent over denominator x open parentheses x to the power of 2 end exponent plus 1 close parentheses end fraction are

      Maths-General
      parallel
      General
      Maths-

      The partial fractions of fraction numerator 1 over denominator x to the power of 3 end exponent left parenthesis x plus 2 right parenthesis end fraction are

      The partial fractions of fraction numerator 1 over denominator x to the power of 3 end exponent left parenthesis x plus 2 right parenthesis end fraction are

      Maths-General
      General
      Maths-

      fraction numerator 3 x to the power of 2 end exponent plus x plus 1 over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end exponent end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator left parenthesis x minus 1 right parenthesis to the power of 2 end exponent end fraction plus fraction numerator C over denominator left parenthesis x minus 1 right parenthesis to the power of 3 end exponent end fraction plus fraction numerator D over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end exponent end fraction then A plus B minus C plus D equals

      fraction numerator 3 x to the power of 2 end exponent plus x plus 1 over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end exponent end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator left parenthesis x minus 1 right parenthesis to the power of 2 end exponent end fraction plus fraction numerator C over denominator left parenthesis x minus 1 right parenthesis to the power of 3 end exponent end fraction plus fraction numerator D over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end exponent end fraction then A plus B minus C plus D equals

      Maths-General
      General
      Maths-

      The partial fractions of fraction numerator x to the power of 2 end exponent over denominator open parentheses x to the power of 2 end exponent plus a to the power of 2 end exponent close parentheses open parentheses x to the power of 2 end exponent plus b to the power of 2 end exponent close parentheses end fraction are

      The partial fractions of fraction numerator x to the power of 2 end exponent over denominator open parentheses x to the power of 2 end exponent plus a to the power of 2 end exponent close parentheses open parentheses x to the power of 2 end exponent plus b to the power of 2 end exponent close parentheses end fraction are

      Maths-General
      parallel
      General
      Maths-

      The partial fractions of fraction numerator 6 x to the power of 4 end exponent plus 5 x to the power of 3 end exponent plus x to the power of 2 end exponent plus 5 x plus 2 over denominator 1 plus 5 x plus 6 x to the power of 2 end exponent end fraction are

      The partial fractions of fraction numerator 6 x to the power of 4 end exponent plus 5 x to the power of 3 end exponent plus x to the power of 2 end exponent plus 5 x plus 2 over denominator 1 plus 5 x plus 6 x to the power of 2 end exponent end fraction are

      Maths-General
      General
      Maths-

      If fraction numerator x to the power of 4 end exponent over denominator left parenthesis x minus a right parenthesis left parenthesis x minus b right parenthesis left parenthesis x minus c right parenthesis end fraction equals P left parenthesis x right parenthesis plus fraction numerator A over denominator x minus a end fraction plus fraction numerator B over denominator x minus b end fraction plus fraction numerator C over denominator x minus c end fraction then P left parenthesis x right parenthesis equals

      If fraction numerator x to the power of 4 end exponent over denominator left parenthesis x minus a right parenthesis left parenthesis x minus b right parenthesis left parenthesis x minus c right parenthesis end fraction equals P left parenthesis x right parenthesis plus fraction numerator A over denominator x minus a end fraction plus fraction numerator B over denominator x minus b end fraction plus fraction numerator C over denominator x minus c end fraction then P left parenthesis x right parenthesis equals

      Maths-General
      General
      Maths-

      Let a,b,c such that fraction numerator 1 over denominator left parenthesis 1 minus x right parenthesis left parenthesis 1 minus 2 x right parenthesis left parenthesis 1 minus 3 x right parenthesis end fraction equals fraction numerator a over denominator 1 minus x end fraction plus fraction numerator b over denominator 1 minus 2 x end fraction plus fraction numerator c over denominator 1 minus 3 x end fraction then ,fraction numerator a over denominator 1 end fraction plus fraction numerator b over denominator 3 end fraction plus fraction numerator c over denominator 5 end fraction equals?

      Let a,b,c such that fraction numerator 1 over denominator left parenthesis 1 minus x right parenthesis left parenthesis 1 minus 2 x right parenthesis left parenthesis 1 minus 3 x right parenthesis end fraction equals fraction numerator a over denominator 1 minus x end fraction plus fraction numerator b over denominator 1 minus 2 x end fraction plus fraction numerator c over denominator 1 minus 3 x end fraction then ,fraction numerator a over denominator 1 end fraction plus fraction numerator b over denominator 3 end fraction plus fraction numerator c over denominator 5 end fraction equals?

      Maths-General
      parallel
      General
      Maths-

      If fraction numerator 2 x plus 1 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent plus 2 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B x plus c over denominator x to the power of 2 end exponent plus 2 end fraction then B=

      If fraction numerator 2 x plus 1 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent plus 2 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B x plus c over denominator x to the power of 2 end exponent plus 2 end fraction then B=

      Maths-General
      General
      Maths-

      If the remainders of the polynomial f(x) when divided by x minus 1 comma x minus 2 are 2,5 then the remainder of f left parenthesis x right parenthesis when divided by left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis is

      If the remainders of the polynomial f(x) when divided by x minus 1 comma x minus 2 are 2,5 then the remainder of f left parenthesis x right parenthesis when divided by left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis is

      Maths-General
      General
      Maths-

      Assertion : f left parenthesis x right parenthesis equals s g n invisible function application left parenthesis x minus vertical line x vertical line right parenthesis can never become positive.
      Reason : f(x) = sgn x is always a positive function.

      Assertion : f left parenthesis x right parenthesis equals s g n invisible function application left parenthesis x minus vertical line x vertical line right parenthesis can never become positive.
      Reason : f(x) = sgn x is always a positive function.

      Maths-General
      parallel
      General
      Maths-

      fraction numerator d x over denominator square root of 1 minus x to the power of 2 end exponent end root minus 1 end fraction=

      fraction numerator d x over denominator square root of 1 minus x to the power of 2 end exponent end root minus 1 end fraction=

      Maths-General
      General
      maths-

      Evaluate not stretchy integral fraction numerator 1 over denominator left parenthesis x to the power of 2 end exponent minus 4 right parenthesis square root of x plus 1 end root end fractiondx

      Evaluate not stretchy integral fraction numerator 1 over denominator left parenthesis x to the power of 2 end exponent minus 4 right parenthesis square root of x plus 1 end root end fractiondx

      maths-General
      General
      maths-

      If f left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x plus l space l n invisible function application square root of 1 plus x end root minus l n square root of 1 minus x end root. The integral of 1 divided by 2 space f apostrophe left parenthesis x right parenthesis with respect to x to the power of 4 end exponent is -

      If f left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x plus l space l n invisible function application square root of 1 plus x end root minus l n square root of 1 minus x end root. The integral of 1 divided by 2 space f apostrophe left parenthesis x right parenthesis with respect to x to the power of 4 end exponent is -

      maths-General
      parallel

      card img

      With Turito Academy.

      card img

      With Turito Foundation.

      card img

      Get an Expert Advice From Turito.

      Turito Academy

      card img

      With Turito Academy.

      Test Prep

      card img

      With Turito Foundation.