Assertion :If roots of the equation x2−bx+c=0 are two consecutive integers, then b2−4c=1 Reason: If a,b,c are odd integer then the roots of the equation 4abcx2+(b2−4ac)x−b=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
Assertion is incorrect but Reason is correct
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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 Assertion :
Given equation x2−bx+c=0 Let α,β be two roots such that |α−β|=1 ⇒(α+β)2−4αβ=1 ⇒b2−4c=1
Reason :
Given equation : 4abcx2+(b2−4ac)x−b=0 D=(b2−4ac)2+16ab2c D=(b2+4ac)2>0 Hence roots are real and distinct.