1

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).

Open in App

Solution

The correct option is **B** Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

p(x)=(k2+4)x2+13x+4k

Let one root of p(x) be α, then other root will be1α

Sum of roots =α+1α=−13k2+4

Product of roots =α×1α=4kk2+4

i.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.

p(x)=(k2+4)x2+13x+4k

Let one root of p(x) be α, then other root will be1α

Sum of roots =α+1α=−13k2+4

Product of roots =α×1α=4kk2+4

i.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.

8

View More

Join BYJU'S Learning Program

Join BYJU'S Learning Program