Question

If one zero of the polynomial f (x) = 5x² + 13x + k is reciprocal of the , other, then the value of k = ……………

B) 5 

C) -5 

D) - 13/5

Answer 1

Correct option is (B) 5

Let \(\alpha\;and\;\frac1\alpha\) are zeros of given polynomial f(x).

\(\therefore\) Product of zeros \(=\frac{\text{constant term}}{\text{coefficient of }x^2}=\frac k5\)

\(\Rightarrow\) \(\alpha.\frac1\alpha\) \(=\frac k5\)

\(\Rightarrow\) \(\frac k5=1\)

\(\Rightarrow\) k = 5

Answer 2

Correct option is B) 5