Question

# Assertion :If 2,3 are the zeroes of a quadratic polynomial, then polynomial is x2−5x+6. Reason: If α,β are the zeroes of a monic quadratic polynomial, then polynomial is x2−(α+β)x+αβ.

A
Both assertion and Reason are correct and reason is the correct explanation for Assertion
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B
Both assertion and reason are correct but reason is not the correct explanation for Assertion
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C
Assertion is correct but reason is incorrect
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D
Assertion is incorrect but reason is correct
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Solution

## The correct option is A Both assertion and Reason are correct and reason is the correct explanation for AssertionAssertionLet f(x)=x2−5x+6f(x)=0⇒ x2−5x+6=0⇒(x−2)(x−3)=0⇒x=2 and x=3∴2,3 are the zeros of the polynomial x2−5x+6∴ Assertion is true.ReasonLet f(x)=x2−(α+β)x+αβf(x)=0⇒x2−(α+β)x+αβ=0⇒(x−α)(x−β)=0⇒x=α and x=β∴α,β are the zeroes of the polynomial x2−(α+β)x+αβ∴ Reason is trueSince, both the Assertion and Reason are true and Reason is a correct explanation for Assertion.The correct answer is A.

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