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Question

Assertion :The equation f(x)=x3+x28x12=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 Assertion
Given, f(x)=x3+x28x+12
Now f(x)=0
Implies (x+2)2(x3)=0
x=2 is the repeated root and x=3
f(x) =3x2+2x8
=(3x4)(x+2)
=0 implies
x=43 and x=2
Hence, assertion and reason are both correct and the reason is the correct explanation of assertion.

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