Question

Assertion :If roots of the equation $x^2-bx+c=0$ are two consecutive integers, then $b^2-4c=1$ Reason: If $a,b,c$ are odd integer then the roots of the equation $4abc{x}^2+(b^2-4ac)x-b=0$ are real and distinct.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is B Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion

Assertion :

Given equation $x^2-bx+c=0$
Let $\alpha ,\beta$ be two roots such that $|\alpha -\beta |=1$
$\Rightarrow (\alpha +\beta {)}^2-4\alpha \beta =1$
$\Rightarrow b^2-4c=1$

Reason :

Given equation :
$4abc{x}^2+(b^2-4ac)x-b=0$
$D=(b^2-4ac{)}^2+16a{b}^{2}c$
$D=(b^2+4ac{)}^2>0$
Hence roots are real and distinct.