Question

if alpha nd beta are the zeros of x^2-6x+k what is the value of k if 3alpha+2beta=20

Answer 1

let f(x) = x^2-6x+k

given ,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 in (i)

3 α +2 β = 20

3 x 8 + 2 β = 20

2 β = -4 => β = -2

Therefore,

αβ =c/a

8 x -2 = k/1 => k/1 = -16

So , k= -16