1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Assertion :If p(x) is a polynomial of degree ≥ 1 and ax+b is a factor of p(x) then we have p(−ba)=0. Reason: If p(x) is a polynomial of degree ≥ 1, then polynomial (x-a)(x-b) is a factor of p(x) if p(a)=0 and p(b)=0.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Assertion is correct but Reason is incorrect
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Both Assertion and Reason are incorrect
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for AssertionLet p(x) be a polynomial of degree≥1.Assertion :If ax+b is a factor of p(x), then :p(x)=(ax+b). q(x) where q(x) is another polynomial of degree≥0.⇒p(−ba)=(a×−ba+b). q(x)=(−b+b). q(x)=0×q(x)=0⇒ Assertion is correct.Reason :(x−a)(x−b) is a factor of p(x), then :p(x)=(x−a)(x−b) q(x).⇒p(a)=(a−a)(a−b) q(x)=0and p(b)=(b−a)(b−b) q(x)=0.⇒ Reason is correct.Reason explains assertion completely.∴ The answer is [A].

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program