Question

If α and β are zeroes of polynomial x square - 6x + a. Find value of "a" if 3α + 2β =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.