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

If the product of the zeroes of the quadratic polynomial \[f(x)=a{{x}^{2}}-6x-6\] is 4, then the value of a is:

A) \[\frac{-3}{2}\]

B) \[\frac{3}{2}\]

C) \[\frac{2}{3}\]

D) \[\frac{-2}{3}\]

Correct Answer: A

Solution :

We have, \[f(x)=a{{x}^{2}}-6x-6\]

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

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4=\frac{-6}{a}\] (given)

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,a=\frac{-3}{2}\]

So, option [a] is correct.