| Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. |
| Assertion [A] If one zero of the polynomial \[p\left( x \right)=\left( k+18 \right){{x}^{2}}+11x+4k\] is the reciprocal of the other zero, then k = 6 |
| Reason [R] If \[\left( x-\alpha \right)\] and \[\left( x-\beta \right)\] are the factor of the polynomial p(x), then \[\alpha \] and \[\beta \]are the zeroes of the p(x) |
A) A is true, R is true; R is a correct explanation for A.
B) A is true, R is true; R is not a correct explanation for A.
C) A is true; R is False.
D) A is false; R is true.
Correct Answer: B
Solution :
| Let \[\alpha ,\,\frac{1}{\alpha }\] be the zeroes of \[p\left( x \right)\], then |
| \[\alpha \,.\,\frac{1}{\alpha }=\frac{4k}{k+18}\] |
| \[\Leftrightarrow \,\,\,\,\frac{4k}{k+18}=1\] |
| \[4k=k+18\] |
| \[3k=18\] |
| \[k=6\] |
| Assertion is true, Reason is true, and Reason is not correct explanation for assertion |
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