First slide

Theory of equations

Question

If the roots of equation $x^{2} + p x + q = 0$ differ by 1, then

Moderate

A

$p^{2} = 4 q$
B

$p^{2} = 4 q + 1$
C

$p^{2} = 4 q - 1$
D

None of these

Solution

Let the roots of the equation be $α, β$
Given $α - β = 1$
$∴ {(α - β)}^{2} = {(α + β)}^{2} - 4 αβ \Rightarrow {(1)}^{2} = {(- p)}^{2} - 4 q$
$∴ p^{2} = 4 q + 1$

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