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Mathematics

Algebra

Easy

Question

If $alpha comma beta$ are the roots of $x squared minus p x plus q equals 0$ and $alpha to the power of apostrophe comma beta to the power of apostrophe$ are the roots of $x squared minus p to the power of apostrophe x plus q to the power of apostrophe equals 0 comma$ then the value of $open parentheses alpha minus alpha to the power of apostrophe close parentheses squared plus open parentheses beta minus alpha to the power of apostrophe close parentheses squared plus open parentheses alpha minus beta to the power of apostrophe close parentheses squared plus open parentheses beta minus beta to the power of apostrophe close parentheses squared$ is

$2 \{p^{2} - 2 q + p^{2} - 2 q^{`} - p p^{`}\}$
$2 \{p^{2} - 2 q + p^{` 2} - 2 q^{`} + q q^{`}\}$
$2 \{p^{2} - 2 q - p^{` 2} - 2 q^{`} + p p^{`}\}$
$2 \{p^{2} - 2 q - p^{` 2} - 2 q^{`} - q q^{`}\}$

The correct answer is: $2 open curly brackets p squared minus 2 q plus p squared minus 2 q to the power of apostrophe minus p p to the power of apostrophe close curly brackets$

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