Question

if alpha and beta are the zeroes of the polynomial x^2 + kx + 45 such that (alpha+beta)^2 = 144, find the value of k.

Answer 1

Step-by-step explanation:

Given quadratic polynomial is p(x) = x2 + kx + 45 Recall that sum of roots of ax2 + bx + c is (−b/a) Hence (α + β) = − (k/1) = − k Given (α + β)2 = 144 ⇒ (- k)2 = 144 ⇒ k2 = 144 ⇒ k = √144 = ± 12

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