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Question

# Assertion :The equation f(x)=x3+x2−8x−12=0 has x=−2 as repeated root. Reason: If the equation f(x)=0 & f′(x)=0 have a common root then roots of f(x)=0 are repeated.

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
Both Assertion and Reason are incorrect
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Solution

## The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for AssertionGiven, f(x)=x3+x2−8x+12Now f(x)=0Implies (x+2)2(x−3)=0x=−2 is the repeated root and x=3f′(x) =3x2+2x−8=(3x−4)(x+2)=0 implies x=43 and x=−2Hence, assertion and reason are both correct and the reason is the correct explanation of assertion.

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