Question

If alpha and beta are zeroes of the polynomial x2 - 6x + a.Find the value of a if 3alpha + 2beta = 20

Answer 1

Polynomial   P(x) = x² - 6 x + a
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 = a  --- (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:    a = α β = -16.