10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

If the zeroes of the quadratic polynomial \[a{{x}^{2}}+x+a\] are equal, then value of a is:

A) \[\frac{1}{2}\]

B) \[-\frac{1}{2}\]

C) \[\pm \frac{1}{2}\]

D) \[\pm 1\]

Correct Answer: D

Solution :

[d] Let \[f(x)=a{{x}^{2}}+x+a\]

Zeroes of the \[f(x)\] are equal

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\alpha \cdot \alpha =\frac{a}{a}\Rightarrow {{\alpha }^{2}}=1\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\alpha =\pm 1\]