Question

a and a/2 are the zero of p(x) = x² + 4x +2a than find the value of a​

Answer 1

Zeroes of p(x) = a, a/2

p(x) = x² + 4x + 2a

We know,

αβ = c/a (Vieta's formula)

{For any polynomial in the form of ax² + bx + c where a ≠ 0 and the zeroes are α & β.}

∴ (a)(a/2) = 2a/1

=> a²/2 = 2a

=> a/2 = 2

=> a = 4.

So, a = 4.