If the roots of the equation $x^{2} - bx + c = 0$ are two consecutive integers, then $b^{2} - 4c$ is

Question

Dr. Abubacker · Accepted Answer

(c)
Let $\alpha$ and $\beta$ are the roots then
$\alpha + \beta = b,\ \alpha\beta = c$
Given, $|\alpha - \beta| = 1$
$\Rightarrow (\alpha + \beta)^{2} - 4\alpha\beta = 1$
$\Rightarrow b^{2} - 4c = 1$

Q. If the roots of the equation $x^{2} - bx + c = 0$ are two consecutive integers, then $b^{2} - 4c$ is

Explanation

Reviewed by Dr. Abubacker

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