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Question

# Assertion (A) If on dividing the polynomial p(x) = x2 − 3ax + 3a − 7 by (x + 1), we get 6 as remainder, then a= 3. Reason (R) When a polynomial p(x) is divided by (x − α), then the remainder is p(α). (a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A). (b) Both assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true.

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Solution

## $\left(\mathrm{d}\right)\text{Assertion}\left(\text{A}\right)\text{is false}\text{.}\phantom{\rule{0ex}{0ex}}\text{By Remainder Theorem, when}p\left(x\right)\text{is divided by}\left(x+1\right)\text{, then the remainder is}p\left(-1\right).\phantom{\rule{0ex}{0ex}}\text{So,}p\left(-1\right)=6\phantom{\rule{0ex}{0ex}}=>{\left(-1\right)}^{2}-3a×\left(-1\right)+3a-7=6\phantom{\rule{0ex}{0ex}}=>6a=12\phantom{\rule{0ex}{0ex}}=>a=2\phantom{\rule{0ex}{0ex}}\therefore \text{Assertion}\left(\text{A}\right)\text{is false}\text{.}\phantom{\rule{0ex}{0ex}}$

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