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Question: Sum of all the values of m for which the roots x<sub>1</sub> and x<sub>2</sub> of the quadratic equa...

Sum of all the values of m for which the roots x1 and x2 of the quadratic equation x2 – 2mx + m = 0 satisfy the condition x13 + x23 = x12 + x22, is –

A

34\frac{3}{4}

B

1

C

94\frac{9}{4}

D

54\frac{5}{4}

Answer

54\frac{5}{4}

Explanation

Solution

x1 + x2 = 2m, x1x2 = m

x13 + x23 = (x1 + x2)3 – 3x1x2 (x1 + x2)

= 8m3 – 3m(2m)

x12 + x22 = (x1 + x2)2 – 2x1x2 = 4m2 – 2m

8m3 – 6m2 = 4m2 – 2m

Ž 8m3 – 10 m2 + 2m = 0

Sum of values = 108\frac{10}{8} = 54\frac{5}{4}.