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Quantitative Aptitude

Functions

If x2+px+q=0 ...

Question

If $x^{2} + p x + q = 0$ has the roots $α and β$ , then the value of ${(α - β)}^{2}$ is

A

$p^{2} - 4 q$

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B

${(p^{2} - 4 q)}^{2}$

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C

$p^{2} + 4 q$

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D

${(p^{2} + 4 q)}^{2}$

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Solution

The correct option is A
$p^{2} - 4 q$

Explanation for the correct option:
In the given equation $x^{2} + p x + q = 0$ , $a = 1, b = p, and c = q$ .
Sum of roots $α + β = - \frac{b}{a} = - p$
Product of roots $α β = \frac{c}{a} = q$
$\begin{array}{rcl} {(α - β)}^{2} & = & {(α + β)}^{2} - 4 α β \\ = & p^{2} - 4 q \end{array}$
Hence, option A is correct.

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