Question

If alpha and beta are the roots of x^2 - 6x + k , find the value of k if 3 alpha - 2 beta =20 .

Answer 1

let f(x) = x2-6x+k

now ,3α + 2β = 20 ……………….(i)

α + 2α + 2β = 20

α +2(α + β) = 20

α + 2(-b/a) = 20

α + 2 { -(-6)/1} = 20

α + 2 x 6 = 20 => α + 12 = 20 => α = 20-12

α = 8

substituting this value of α in (i)

3 α +2 β = 20 => 3 x 8 + 2 β = 20

2 β = -4 => β = -2

α β = c/a => 8 x -2 = k/1 => k/1 = -16

So , k= -16