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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.

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Solution

The correct option is **A** Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Let p(x) be a polynomial of degree≥1.

Let 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].

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