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

# Assertion :If one zero of polynomial p(x)=(k2+4)x2+13x+4k is reciprocal of other, then k=2. Reason: If x−α is a factor of p(x), then p(α), then p(α)=0 i.e. α is a zero of p(x).

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

## The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertionp(x)=(k2+4)x2+13x+4kLet one root of p(x) be α, then other root will be1α Sum of roots =α+1α=−13k2+4Product of roots =α×1α=4kk2+4i.e. 4kk2+4=1⇒ 4k=k2+4⇒ k2+4−4k=0⇒ (k−2)2=0⇒ k−2=0⇒ k=2∴ Assertion is correct.Also, if (x−α) is a factor of p(x), it means α is a root of p(x).∴p(α)=0 or α is a zero of p(x).Thus, Reason is also correct but it is not the correct explanation for assertion.

Suggest Corrections
8
Join BYJU'S Learning Program
Related Videos
MATHEMATICS
Watch in App
Join BYJU'S Learning Program