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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.

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.

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Mathematics
2 years
2021-07-08T05:30:23+00:00
2021-07-08T05:30:23+00:00 1 Answers
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## Answers ( )

Answer:Given equation:

ax2+bx+c=0

Letαandβbe the roots of given quadratic equationSum 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 rootsi.e.i.e.−b/a =(α+β)²−2αβi.e.a−b= ( a−b ) 2−a2ci.e.−ab=b²−2aci.e.ab+b² =2acHENCE,PROVED.

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