Question

Assertion: If (x − 2) is a factor p(x) = x³ − 2x + 3k, then $k=\frac{-4}{3}$.
Reason: If p(x) is divided by (x − a), then the remainder is p(a).

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true and but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Answer 1

(b) Both Assertion and Reason are true, but Reason is not a correct explanation of Assertion.

Assertion:
Let:
$p\left(x\right)=x^3-2x+3k$
Now,
$x-2=0\Rightarrow x=2$
$$\begin{gathered} \left(x-2\right)\text{is a factor of}p\left(x\right). \\ \Rightarrow p\left(2\right)=0 \\ \Rightarrow 2^3-2\times 2+3k=0 \\ \Rightarrow 8-4+3k=0 \\ \Rightarrow 4+3k=0 \\ \Rightarrow k=\frac{-4}{3} \end{gathered}$$
Hence, Assertion is true.
Reason: If p(x) is divided by (x − a), then the remainder is p(a).
The given statement is true, but it is not correct explanation of Assertion.
Therefore, both Assertion and Reason are true, but Reason is not a correct explanation of Assertion.