If one zero of the polynomial f (x) = (k 2 + 4) x 2 + 13x + 4k is reciprocal of the other, then k =

Question

Philoid · Accepted Answer

Given;

f(x) = (k² + 4) x² + 13x + 4k,

One zero of the polynomial is reciprocal of the other,

Let a be the one zero,

∴ The other zero will be 1/a

As we know that,

Product of the zeros = c/a = 4k/k² + 4

∴ 4k/k² + 4 = 1

⇒ 4k = k² + 4

⇒ k² + 4 – 4k = 0

⇒ (k – 2)² = 0

⇒ k = 2

So the value of k is 2