Question

In ax² + bx + c = 0, if the sum of the roots is equal to the sum of their squares, then show that

2ac = ab + b².​

Answer 1

Answer:

Given equation:

ax2+bx+c=0

Let α and β be the roots of given quadratic equation

Sum of the roots i.e. α+β= -b/a

Product of roots i.e. αβ= c/a

It is given that,

Sum of the roots = Sum of squares of the roots

i.e. −b/a =α² +β²

i.e. −b/a =(α+β)²−2αβ

i.e. a−b= ( a−b ) 2−a2c

i.e. −ab=b²−2ac

i.e. ab+b² =2ac

HENCE,PROVED.

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