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Question

The quadratic equation whose roots are I and m where l= $lim for theta not stretchy rightwards arrow 0 of open parentheses fraction numerator 3 sin space theta minus 4 sin cubed space theta over denominator theta end fraction close parentheses m equals lim for theta not stretchy rightwards arrow 0 of open parentheses fraction numerator 2 tan space theta over denominator theta open parentheses 1 minus tan squared space theta close parentheses end fraction close parentheses$ is

$x^{2} - 5 x - 6 = 0$
$x^{2} - 5 x + 6 = 0$
$x^{2} + 5 x - 6 = 0$
$x^{2} + 5 x + 6 = 0$

hint Hint:

In this question, we have to find the quadratic equation where the roots l and m are given. First we will find the value of l and m. Then to find the quadratic equation when l and m are roots we will use the form $x squared minus left parenthesis l plus m right parenthesis x plus l m equals 0$ .

The correct answer is: $x squared minus 5 x plus 6 equals 0$

Given, the quadratic equation whose roots are I and m where
l = $lim for theta not stretchy rightwards arrow 0 of open parentheses fraction numerator 3 sin space theta minus 4 sin cubed space theta over denominator theta end fraction close parentheses m equals lim for theta not stretchy rightwards arrow 0 of open parentheses fraction numerator 2 tan space theta over denominator theta open parentheses 1 minus tan squared space theta close parentheses end fraction close parentheses$
$l equals limit as theta rightwards arrow 0 of open parentheses fraction numerator 3 space sin theta minus 4 sin cubed theta over denominator theta end fraction close parentheses space space space space space space space space space space space space space space space space space space space space m equals limit as theta rightwards arrow 0 of open parentheses fraction numerator 2 tan theta over denominator theta left parenthesis 1 minus tan squared theta right parenthesis end fraction close parentheses space equals limit as theta rightwards arrow 0 of open parentheses fraction numerator sin space 3 theta over denominator theta end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as theta rightwards arrow 0 of open parentheses fraction numerator tan space 2 theta over denominator theta end fraction close parentheses space equals limit as theta rightwards arrow 0 of open parentheses fraction numerator sin space 3 theta over denominator 3 theta end fraction close parentheses cross times 3 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as theta rightwards arrow 0 of space open parentheses fraction numerator sin 2 theta over denominator theta cos 2 theta end fraction close parentheses space equals 1 cross times 3 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as theta rightwards arrow 0 of open parentheses fraction numerator sin 2 theta over denominator 2 theta end fraction close parentheses cross times 2 cross times fraction numerator 1 over denominator cos 2 theta end fraction space equals 3 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 l equals 3 space a n d space m equals 2 t h e space q u a d t r a t i c space e q u a t i o n space w h e n space t h e space r o o t s space a r e space g i v e n equals x squared minus left parenthesis l plus m right parenthesis x plus l m equals x squared minus left parenthesis 3 plus 2 right parenthesis x plus left parenthesis 3 cross times 2 right parenthesis equals x squared minus 5 x plus 6 space$

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