Question

Pls answer this question.

Answer 1

Answer:

GIVEN EQUATION :–

$a {x}^{2} + bx + c = 0$

it's roots are –

$\alpha \: \: and \: \: \beta$

TO FIND :–

${( \frac{1}{ { \alpha }^{2} } - \frac{1}{ { \beta }^{2} } ) }^{2}$

SOLUTION :–

$= {( \frac{1}{ { \alpha }^{2} } - \frac{1}{ { \beta }^{2} }) }^{2} \\ \\ = {( \frac{ { \alpha }^{2} - { \beta }^{2} }{ {( \alpha \beta )}^{2} }) }^{2} \\ \\ = \frac{ {( \alpha + \beta )}^{2}{( \alpha - \beta )}^{2} }{ {( \alpha \beta )}^{4} } \\ \\ = \frac{ {( \frac{ - b}{a} )}^{2} {( \frac{ \sqrt{d} }{a} )}^{2}}{( { \frac{c}{a} )}^{4} } \\ \\ = \frac{ (\frac{ {b}^{2} }{ {a}^{2} } ) \frac{( {b}^{2} - 4ac) }{( {a}^{2}) } }{ { (\frac{c}{a}) }^{4} } \\ \\ = \frac{ ({b}^{2})( {b}^{2} - 4ac) }{ {c}^{4} }$

☆☆☆ OPTION (D) IS CORRECT ☆☆☆

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