10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

If the product of the zeroes of the quadratic polynomial \[{{x}^{2}}-3ax+2{{a}^{2}}-1\] is 7, then a is equal to:

A) \[\pm 1\]

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

C) \[\pm 2\]

D) \[\pm 3\]

Correct Answer: C

Solution :

[c] Let \[f(x)={{x}^{2}}-3ax+2{{a}^{2}}-1\]

Given, product of zeroes =7

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{(2{{a}^{2}}-1)}{1}=7\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2{{a}^{2}}-1=7\Rightarrow 2{{a}^{2}}=8\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{a}^{2}}=4\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,a=\pm 2\]