    Question

# Assertion: If (x − 1) is a factor of p(x) = x2 + kx + 1, then k = −2. Reason: If (x − a) is a factor of p(x), then p(a) = 0. (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.

Open in App
Solution

## (a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion. Assertion: Let: $p\left(x\right)={x}^{2}+kx+1\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$ Now, $x-1=0⇒x=1$ $\left(x-1\right)\text{is a factor of}p\left(x\right).\phantom{\rule{0ex}{0ex}}⇒p\left(1\right)=0\phantom{\rule{0ex}{0ex}}⇒{1}^{2}+k×1+1=0\phantom{\rule{0ex}{0ex}}⇒1+k+1=0\phantom{\rule{0ex}{0ex}}⇒k+2=0\phantom{\rule{0ex}{0ex}}⇒k=-2$ Hence, Assertion is true. Reason: If (x − a) is a factor of p(x), then p(a) = 0. The given statement is true. Therefore, both Assertion and Reason are true and Reason is a correct explanation of Assertion.  Suggest Corrections  1      Related Videos   MATHEMATICS
Watch in App  Explore more