Question

if alpha and beta are the zeros of the quadratic equation X square - 6 X + K is equals to zero find the value of k if 3 alpha + 2 Beta is equals to 20​

Answer 1

Polynomial   P(x) = x² - 6 x + k

Given  α and  β  are the roots.     To find a , if 3 α + 2 β = 20.  ---(1)

From the quadratic expression:

    α + β = 6       ---(2)

    and   α β = k  --- (3)

Multiply equation (2) by 2 and subtract from (1) to get:

    α = 20 -12 = 8

Substitute this value in(2) to get:    

     β = 6-8 = -2   

Substitute these in (3) to get:    k = α β = -16.