If ${x^2} + px + q = 0$ has the roots $\alpha \;{\rm{and}}\;\beta $, then the value of ${\left( {\alpha - \beta } \right)^2}$ is equal to

${\left( {{p^2} - 4q} \right)^2}$

${\left( {{p^2} + 4q} \right)^2}$

JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

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Application +4 | -1

{x^2} + px + q = 0

has the roots

\alpha \;\mathrm{and}\;\beta

, then the value of

{\left( {\alpha - \beta } \right)^2}

is equal to

View answer and explanation

Correct option: A

{p^2} - 4q

Option A (

{p^2} - 4q

) is correct because it is the simplified form of the expression

(\alpha - \beta)^2

using the relationship between roots and coefficients of a quadratic equation.

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