| Assertion (A): If one zero of polynomial\[p(x)=({{k}^{2}}+4){{x}^{2}}+13x+4k\]is reciprocal of other, then \[k=2\]. |
| Reason (R): If \[(x-\alpha )\] is a factor of \[p(x),\] then \[p(\alpha )=0\]i.e., \[\alpha \]is a zero of \[p(x)\]. |
A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C) Assertion (A) is true but reason (R) is false.
D) Assertion (A) is false but reason (R) is true.
Correct Answer: B
Solution :
| [b] Let \[\alpha ,\frac{1}{\alpha }\]be the zeroes of \[p(x),\] then |
| \[\alpha \cdot \frac{1}{\alpha }=\frac{4k}{{{k}^{2}}+4}\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,\,\,1=\frac{4k}{{{k}^{2}}+4}\] |
| \[{{k}^{2}}-4k+4=0\,\,\,\,\,\,\,\Rightarrow \,\,\,{{(k-2)}^{2}}=0\] |
| \[k=2\] |
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