If the sum of the roots of the equation `ax^(2) + bx+ c = 0` is equal to the sum of their squares then

Options

A. `a^(2) + b^(2) = c^(2)`
B. `a^(2) + b^(2) = a + b`
C. `ab+ b^(2) = 2ac`
D. `ab-b^(2) = 2ac`

Answer

C

Explanation

`ax^(2) + bx + c = 0 `
Let the root be `alpha and beta`
` alpha + beta = -b/a, alpha.beta = c/a`
` rArr alpha + beta = alpha^(2) + beta^(2) " "`…(given)
` rArr alpha+beta = (alpha + beta)^(2) - 2 alpha beta `
` rArr -b/a = (-b/a)^(2) - (2c)/a`
` rArr b^(2) + ab = 2ac`