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Question

Assertion :If one zero of polynomial p(x)=(k2+4)x2+13x+4k is reciprocal of other, then k=2. Reason: If xα is a factor of p(x), then p(α), then p(α)=0 i.e. α is a zero of p(x).

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
p(x)=(k2+4)x2+13x+4k
Let one root of p(x) be α, then other root will be1α
Sum of roots =α+1α=13k2+4
Product of roots =α×1α=4kk2+4
i.e. 4kk2+4=1
4k=k2+4
k2+44k=0
(k2)2=0
k2=0
k=2
Assertion is correct.
Also, if (xα) is a factor of p(x), it means α is a root of p(x).
p(α)=0 or α is a zero of p(x).
Thus, Reason is also correct but it is not the correct explanation for assertion.

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