Question

If alpha and beta are the zeroes of the polynomials x^2 -6x +k and 3 alpha +2beta = 20. Find k

Answer 1

Given,

α and β are the zeroes of the polynomial x² - 6x + k

∴α + β = -(-6)/1 = 6

Also,
αβ = k/1 = k

Now,

3α + 2β = 20

⇒ 3(6) + 2(k) = 20

⇒ 18 + 2k = 20

⇒ 9 + 2k = 10

⇒ 2k = 1

⇒ k = 1/2