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Question

Assertion :If roots of the equation x2bx+c=0 are two consecutive integers, then b24c=1 Reason: If a,b,c are odd integer, then the roots of the equation 4abcx2+(b24ac)xb=0 are real and distinct.

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 B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
According to statement 1, given equation is

x2bx+c=0

Let α,β be two roots such that

|αβ|=1

(α+β)24αβ=1

b24c=1

According to statement 2, given equation is 4abcx2+(b24ac)xb=0.

Hence

D=(b24ac)2+16ab2c

=(b2+4ac)2>0

Hence, roots are real and unequal.

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