If and are the roots of the equation x2 px q 0 then what is 2 equal to ........

Quantitative Aptitude (CDS) Quadratic Equations

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If $\alpha$ and $\beta$ are the roots of the equation x² + px + q = 0, then what is $\alpha$ ² + $\beta^{2}$ equal to?

p²- 2q

q²- 2p

p²+ 2q

p²- q

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Explanation:

According to question,
Sum of root $(\alpha+\beta)$ = −b/a
So, $(\alpha+\beta)$ = −p ……….. (i)
Product of root (???? =??/??)
$=>(\alpha\beta)=q...................(ii)$
From (i)
$(\alpha+\beta)$ = - p
$(\alpha+\beta)^{2}=b^{2}$
$=>\alpha^{2}+\beta^{2}+2\alpha\beta=p^{2}$
$=>\alpha^{2}+\beta^{2}= p^{2}-2\alpha\beta$
$=>\alpha^{2}+\beta^{2}= p^{2}-2q$
Hence option(1) is the answer.