Question

# Assertion: If p(x) = x3 − ax2 + 6x − a is divided by (x − a), then the remainder is 5a. 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.

Open in App
Solution

## (a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion. Assertion: Let: $p\left(x\right)={x}^{3}-a{x}^{2}+6x-a$ Now, $x-a=0⇒x=a$ By the remainder theorem, we know that when $p\left(x\right)\text{is divided by}\left(x-a\right),\text{the remainder is}p\left(a\right).$ Now, we have: $p\left(a\right)={a}^{3}-a×{a}^{2}+6×a-a\phantom{\rule{0ex}{0ex}}={a}^{3}-{a}^{3}+6a-a\phantom{\rule{0ex}{0ex}}=5a$ Hence, Assertion is true. Reason: If p(x) is divided by (x − a), then the remainder is p(a). The given statement is true. Therefore, both Assertion and Reason are true and Reason is a correct explanation of Assertion.

Suggest Corrections
0
Join BYJU'S Learning Program
Select...
Related Videos
AM and GM
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
Select...