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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Reagan 2 years 2021-07-08T05:30:23+00:00 1 Answers 0 views 0

Answers ( )

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    2021-07-08T05:32:21+00:00

    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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