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.​

1 thought on “In ax² + bx + c = 0, if the sum of the roots is equal to the sum of their squares, then show that<br /><br />2ac = ab + b².​”

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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