If one zero of the polynomial f (x) = (k2 + 4) x2 + 13x + 4k is recipr

1.	If one zero of the polynomial f (x) = (k2 + 4) x2 + 13x + 4k is reciprocal of the other, then k =A. 2B. – 2C. 1D. – 1
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 ⇒ k ² + 4 – 4k = 0 ⇒ (k – 2)² = 0 ⇒ k = 2 So the value of k is 2

If one zero of the polynomial f (x) = (k2 + 4) x2 + 13x + 4k is reciprocal of the other, then k =A. 2B. – 2C. 1D. – 1

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

⇒ k ² + 4 – 4k = 0

⇒ (k – 2)² = 0

⇒ k = 2

So the value of k is 2