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

A quadratic polynomial whose one zero is \[-3\] and product of zeroes is 0, is:

A) \[3{{x}^{2}}+3\]

B) \[{{x}^{2}}-3x\]

C) \[{{x}^{2}}+3x\]

D) \[3{{x}^{2}}-3\]

Correct Answer: C

Solution :

Let \[\alpha \] and \[\beta \] be the zeroes of the required polynomial.

Given, \[\alpha =-3\]and \[\alpha \cdot \beta =0\]

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,-3\cdot \beta =0\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\beta =0\]

Now, required polynomial

\[={{x}^{2}}-(\alpha +\beta )x+\alpha \beta \]

\[={{x}^{2}}-(-3+0)x+(-3)\,(0)={{x}^{2}}+3x\]

So, option [c] is correct.