Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito 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

Mathematics

Algebra

Easy

Question

If $alpha comma beta comma gamma comma delta$ are the roots of the equation $x to the power of 4 minus K x cubed plus K x squared plus L x plus M equals 0$ ,where K, L, M are real numbers, then the minimum value of $alpha squared plus beta squared plus gamma squared plus delta squared$ is

0
-1
1
2

The correct answer is: -1

Related Questions to study

If $alpha comma beta comma gamma$ are the roots of $x cubed minus x squared minus 1 equals 0$ then the value $left parenthesis 1 plus alpha right parenthesis divided by left parenthesis 1 minus alpha right parenthesis plus left parenthesis 1 plus beta right parenthesis divided by left parenthesis 1 minus beta right parenthesis plus left parenthesis 1 plus gamma right parenthesis divided by left parenthesis 1 minus gamma right parenthesis$ is equal to

If $alpha comma beta comma gamma$ are the roots of $x cubed minus x squared minus 1 equals 0$ then the value $left parenthesis 1 plus alpha right parenthesis divided by left parenthesis 1 minus alpha right parenthesis plus left parenthesis 1 plus beta right parenthesis divided by left parenthesis 1 minus beta right parenthesis plus left parenthesis 1 plus gamma right parenthesis divided by left parenthesis 1 minus gamma right parenthesis$ is equal to

MathematicsAlgebra

If $1 over 1 squared plus 1 over 2 squared plus 1 over 3 squared plus horizontal ellipsis horizontal ellipsis. infinity equals pi squared over 6$ ,then $1 over 1 squared plus 1 over 2 squared plus 1 over 3 squared plus 1 over 5 squared horizontal ellipsis horizontal ellipsis$ equals

If $1 over 1 squared plus 1 over 2 squared plus 1 over 3 squared plus horizontal ellipsis horizontal ellipsis. infinity equals pi squared over 6$ ,then $1 over 1 squared plus 1 over 2 squared plus 1 over 3 squared plus 1 over 5 squared horizontal ellipsis horizontal ellipsis$ equals

MathematicsAlgebra

If $a subscript 1 comma a subscript 2 midline horizontal ellipsis midline horizontal ellipsis times a subscript n$ are in H.P. then $fraction numerator a subscript 1 over denominator a subscript 2 plus a subscript 3 plus horizontal ellipsis plus a subscript n end fraction comma fraction numerator a subscript 2 over denominator a subscript 2 plus a subscript 3 plus horizontal ellipsis plus a subscript n end fraction comma horizontal ellipsis..... fraction numerator a subscript n over denominator a subscript 1 plus a subscript 2 plus horizontal ellipsis plus a subscript n minus 1 end subscript end fraction$ are in

If $a subscript 1 comma a subscript 2 midline horizontal ellipsis midline horizontal ellipsis times a subscript n$ are in H.P. then $fraction numerator a subscript 1 over denominator a subscript 2 plus a subscript 3 plus horizontal ellipsis plus a subscript n end fraction comma fraction numerator a subscript 2 over denominator a subscript 2 plus a subscript 3 plus horizontal ellipsis plus a subscript n end fraction comma horizontal ellipsis..... fraction numerator a subscript n over denominator a subscript 1 plus a subscript 2 plus horizontal ellipsis plus a subscript n minus 1 end subscript end fraction$ are in

MathematicsAlgebra

parallel

If x, y, z real and $4 x squared plus 9 y squared plus 16 z squared minus 6 x y minus 12 y z minus 8 z x equals 0$ , then x, y, z are in

If x, y, z real and $4 x squared plus 9 y squared plus 16 z squared minus 6 x y minus 12 y z minus 8 z x equals 0$ , then x, y, z are in

MathematicsAlgebra

If x,2y,3z are in A.P. where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is

If x,2y,3z are in A.P. where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is

MathematicsAlgebra

If $a squared plus b squared comma a b plus b c$ and $b squared plus c squared$ are in G.P., then a, b, c in

If $a squared plus b squared comma a b plus b c$ and $b squared plus c squared$ are in G.P., then a, b, c in

MathematicsAlgebra

parallel

Let $a subscript 1 comma a subscript 2 comma a subscript 3 comma horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis$ be terms of an A.P. If $fraction numerator a subscript 1 plus a subscript 2 plus horizontal ellipsis horizontal ellipsis a subscript p over denominator a subscript 1 plus a subscript 2 plus horizontal ellipsis horizontal ellipsis a subscript 9 end fraction equals p squared over q squared comma p not equal to q$ then $a subscript 6 over a subscript 21$ equals

Let $a subscript 1 comma a subscript 2 comma a subscript 3 comma horizontal ellipsis midline horizontal ellipsis midline horizontal ellipsis$ be terms of an A.P. If $fraction numerator a subscript 1 plus a subscript 2 plus horizontal ellipsis horizontal ellipsis a subscript p over denominator a subscript 1 plus a subscript 2 plus horizontal ellipsis horizontal ellipsis a subscript 9 end fraction equals p squared over q squared comma p not equal to q$ then $a subscript 6 over a subscript 21$ equals

MathematicsAlgebra

In an A.P. of which a is the first term, if the sum of the first p terms is zero, then the sum of the next q terms is

In an A.P. of which a is the first term, if the sum of the first p terms is zero, then the sum of the next q terms is

MathematicsAlgebra

Suppose a, b, c, d and 2ac=b+d. Consider the quadratic equations $x squared plus 2 a x plus b equals 0$ and $x squared plus 2 c x plus d equals 0$ .Then

Suppose a, b, c, d and 2ac=b+d. Consider the quadratic equations $x squared plus 2 a x plus b equals 0$ and $x squared plus 2 c x plus d equals 0$ .Then

MathematicsAlgebra

parallel

The least integral value $alpha$ of x such that $fraction numerator x minus 5 over denominator x squared plus 5 x minus 14 end fraction greater than 0$ , satisfies

The least integral value $alpha$ of x such that $fraction numerator x minus 5 over denominator x squared plus 5 x minus 14 end fraction greater than 0$ , satisfies

MathematicsAlgebra

The non-integral roots of $x to the power of 4 minus 3 x cubed minus 2 x squared plus 3 x plus 1 equals 0$ are

The non-integral roots of $x to the power of 4 minus 3 x cubed minus 2 x squared plus 3 x plus 1 equals 0$ are

MathematicsAlgebra

The value of a for which one root of a for which of the equation $x squared minus left parenthesis a plus 1 right parenthesis x plus a squared plus a minus 8 equals 0$ exceeds 2 and other is less then 2, are given by

The value of a for which one root of a for which of the equation $x squared minus left parenthesis a plus 1 right parenthesis x plus a squared plus a minus 8 equals 0$ exceeds 2 and other is less then 2, are given by

MathematicsAlgebra

parallel

Let A(2,-3) and B(-2,1) be vertices of a right ABC. If the centroid of this triangle moves on the line, 2x+3y=1, then the locus of the vertex C is the line

Let A(2,-3) and B(-2,1) be vertices of a right ABC. If the centroid of this triangle moves on the line, 2x+3y=1, then the locus of the vertex C is the line

MathematicsAlgebra

If the sum and product of the first three terms in AP are 33 and 1155, respectively, then a value of its 11^th term is

If the sum and product of the first three terms in AP are 33 and 1155, respectively, then a value of its 11^th term is

MathematicsAlgebra

Let the sum of the first n terms of a non- constant AP $a subscript 1 comma a subscript 2 comma a subscript 3 horizontal ellipsis horizontal ellipsis$ be $50 n plus fraction numerator n left parenthesis n minus 7 right parenthesis over denominator 2 end fraction A comma$ where A is a constant, If d is the common difference of this AP, then the ordered pair $open parentheses d comma a subscript 50 close parentheses$ is equal to

Let the sum of the first n terms of a non- constant AP $a subscript 1 comma a subscript 2 comma a subscript 3 horizontal ellipsis horizontal ellipsis$ be $50 n plus fraction numerator n left parenthesis n minus 7 right parenthesis over denominator 2 end fraction A comma$ where A is a constant, If d is the common difference of this AP, then the ordered pair $open parentheses d comma a subscript 50 close parentheses$ is equal to

MathematicsAlgebra

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.