10th Class Mathematics Polynomials Question Bank Case Based (MCQs) - Polynomials

If one zero of the polynomial \[f(x)=5{{x}^{2}}+13x+m\] is reciprocal of the other, then the value of m is:

A) 6

B) 0

C) 5

D) 1

Correct Answer: C

Solution :

Since one zero of the polynomial f(x) is reciprocal of the other, then

Product of zeroes \[=\frac{\text{Constant term}}{\text{Coefficient of }{{\text{x}}^{2}}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\alpha \cdot \frac{1}{\alpha }=\frac{m}{5}\Rightarrow m=5\]

So, option [c] is correct.