Mathematics
Grade10
Easy

Question

If f left parenthesis x right parenthesis equals x squared plus 8 x plus c  and g left parenthesis x right parenthesis equals x squared plus 10 x plus d  are perfect square trinomials, find f (1) + g (1).

  1. 60
  2. 61
  3. 63
  4. 64

hintHint:

An expression obtained from the square of the binomial equation is a perfect square trinomial.

The correct answer is: 61


    y equals x squared plus 8 x plus c
    Now open parentheses b over 2 close parentheses squared equals open parentheses 8 over 2 close parentheses squared equals 16
    Add 16 to x squared plus 8 x, we get
    x squared plus 8 x plus 16 equals left parenthesis x plus 4 right parenthesis squared is binomial squared
    Since it is given that the expression is a perfect square trinomial, the value of c will be 16.
    y equals x squared plus 10 x plus d
    Now open parentheses b over 2 close parentheses squared equals open parentheses 10 over 2 close parentheses squared equals 25
    Add 25 to x squared plus 10 x, we get
    x squared plus 10 x plus 25 equals left parenthesis x plus 5 right parenthesis squared is binomial squared
    Since it is given that the expression is a perfect square trinomial, the value of d will be 25.
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell f left parenthesis 1 right parenthesis plus g left parenthesis 1 right parenthesis end cell cell equals left parenthesis 1 plus 4 right parenthesis squared plus left parenthesis 1 plus 5 right parenthesis squared end cell row blank cell equals 25 plus 36 end cell row blank cell equals 61 end cell end table

    If a trinomial is in the form ax 2 + bx + c is said to be a perfect square, if and only if it satisfies the condition b 2 = 4ac.

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