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.

Answer 1

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