The equation formed by multiplying each root of `ax^(2) + bx+ c = 0" by "2 " is "x^(2) = 36x + 24 =0`
What is the sum of the squares of the roots of the equation `x^(2) + 2x-143 =0`

Options

A. 170
B. 180
C. 190
D. 290

Answer

D

Explanation

Let ` alpha, beta` be the roots of given equation
then `alpha + beta = -2`
and `alpha beta = - 143`
Consider `alpha^(2) + beta^(2) = ( alpha + beta)^(2) - 2 alpha beta`
`= (-2)^(2) - 2 (-143) = 4 + 286 = 290`