Math, asked by thuthujis, 9 months ago

Please help. Functions question.

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Answered by kailashmeena123rm

$<!DOCTYPE html><html><body> <h1 style="font-size:10vw;">Answer</h1><h2 style="font-size:8vw;">useful concept</h2> we have to find that value of a for which graph of function intersect x axis or that value for which roots of quadratic equations exist. Actually graph of quadratic equation follow a parabolic path and point of intersection of graph and x - axis goves roots of the equation. <h2 style="font-size:8vw;">solution</h2></body></html>$

here we can apply two coditions

first

$\\ \\ \star \: \: \: a - \frac{1}{a} \ne \: 0 \\ \star \: \: discriminent \: \geqslant 0 \\ \\$

from first

$\\ a \ne \: \pm1 \\ \\$

from second

$\\ \rightarrow \: D \geqslant 0 \\ \\$

$\rightarrow \: \: {8}^{2} - 4(a - \frac{1}{a} )(9a) \geqslant 0 \\ \\\rightarrow \: 64 - 36a(a - \frac{1}{a} ) \\ \\ \rightarrow \: 100 - 36 {a }^{2} \geqslant 0 \\ \\$

use wavy curve method or any other me this to solve inequality

$\\ \\$

we get

$\\ a \in( - \infty, - \frac{5}{3} ] \cup [ \frac{5}{3} , \infty) \\ \\$

option (a)

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