10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

If one zero of the quadratic polynomial \[\text{2}{{\text{x}}^{2}}-\text{6kx}+\text{6x}-\text{7}\]is negative of the other, then k is equal to:

A) \[-1\]

B) \[1\]

C) \[0\]

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

Correct Answer: B

Solution :

[b] Let \[f(x)=2{{x}^{2}}-6kx+6x-7\]

\[=2{{x}^{2}}-6(k-1)x-7\]

Given, one zero of \[f(x)\] is negative of the other.

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\alpha +(-\alpha )=-\left\{ \frac{-6(k-1)}{2} \right\}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3(k-1)=0\Rightarrow \,\,k=1\]