10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

The number of value of k for which the quadratic polynomial \[k{{x}^{2}}+x+k\]has equal zeroes is

A) 4

B) 1

C) 2

D) 3

Correct Answer: C

Solution :

Let \[f\left( x \right)=k{{x}^{2}}+x+k\]

For equal roots. Its discriminant should be zero i.e. \[D={{b}^{2}}-4ac=0\]

\[\Rightarrow \,\,\,\,1-4k\,.\,k=0\,\,\Rightarrow k=\pm \frac{1}{2}\]

So, for two values of k, given quadratic polynomial has equal zeroes.