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Question

Assertion :If 2,3 are the zeroes of a quadratic polynomial, then polynomial is x25x+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 Assertion
Assertion
Let f(x)=x25x+6
f(x)=0 x25x+6=0
(x2)(x3)=0
x=2 and x=3
2,3 are the zeros of the polynomial x25x+6
Assertion is true.
Reason
Let f(x)=x2(α+β)x+αβ
f(x)=0x2(α+β)x+αβ=0
(xα)(xβ)=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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