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.

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Solution

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

**Assertion**

Let f(x)=x2−5x+6

f(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.

**Reason**

Let f(x)=x2−(α+β)x+αβ

f(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 true

Since, both the Assertion and Reason are true and Reason is a correct explanation for Assertion.

The correct answer is A.

f(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.

f(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 true

Since, both the Assertion and Reason are true and Reason is a correct explanation for Assertion.

The correct answer is A.

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