If one zero of the polynomial f(x) = (k2+4) x2 + 13x +4k is reciprocal of the other, k = - Maths - Polynomials

Question

If one zero of the polynomial f(x) = (k2+4)
x2 + 13x +4k is reciprocal of the other,
k =
a) 2 b) -2 c) 1 d) -1
ans: a) 2

Shridhar Kaushik · Accepted Answer

Given that one zero of the polynomial

f (x) = (k² + 4) x² +13x + 4k is reciprocal of the other.

Let α be the one zero.

∴ The other zero will be $\frac{1}{α}$ .

We know that,

$Product of zeroes = \frac{c}{a} = \frac{4 k}{k^{2} + 4} ∴ \frac{4 k}{k^{2} + 4} = 1 \Rightarrow 4 k = k^{2} + 4 \Rightarrow k^{2} + 4 - 4 k = 0 \Rightarrow (k - 2)^{2} = 0 \Rightarrow k = 2$

Hence, the value of k is 2.

If one zero of the polynomial f(x) = (k2+4) x2 + 13x +4k is reciprocal of the other, k = a) 2 b) -2 c) 1 d) -1 ans: a) 2

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

k =

a) 2 b) -2 c) 1 d) -1

ans: a) 2