If - are the roots of the quadratic equation ax2-bx-c-0-a0- Find the equation with roots 1- and 1-

Given: nbsp;ax^2+bx+c=0,a0 with roots α,β To find: Transformed quadratic equation with roots 1α and 1β Let,t=1x Since, x=α⇒ t=1α nbsp; nbsp; nbsp; ...

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Standard XII

Mathematics

Relations Between Roots and Coefficients

If α,β are th...

Question

If $α, β$ are the roots of the quadratic equation $a x^{2} + b x + c = 0, a \neq 0$ . Find the equation with roots $\frac{1}{α}$ and $\frac{1}{β} .$

{(\frac{a}{x})}^{2} + (\frac{b}{x}) + c = 0

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a {(\frac{1}{x})}^{2} + b (\frac{1}{x}) + c = 0

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a {(\frac{1}{x})}^{2} + b (\frac{1}{x}) + c x = 0

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None of the above

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Solution

The correct option is B $a {(\frac{1}{x})}^{2} + b (\frac{1}{x}) + c = 0$
Given: $a x^{2} + b x + c = 0, a \neq 0$ with roots $α, β$
To find: Transformed quadratic equation with roots $\frac{1}{α}$ and $\frac{1}{β}$

Let, $t = \frac{1}{x}$

Since, $x = α \Rightarrow t = \frac{1}{α}$
$x = β \Rightarrow t = \frac{1}{β}$

Replace $x \to \frac{1}{t}$

$a {(\frac{1}{t})}^{2} + b (\frac{1}{t}) + c = 0$

In terms of variable x,

$a {(\frac{1}{x})}^{2} + b (\frac{1}{x}) + c = 0$
This is required equation.

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If α,β are the roots of the quadratic equation ax2+bx+c=0,a≠0. Find the equation with roots 1α and 1β.

The correct option is B a(1x)2+b(1x)+c=0 Given: ax2+bx+c=0,a≠0 with roots α,β To find: Transformed quadratic equation with roots 1α and 1β Let,t=1x Since, x=α⇒t=1α x=β⇒t=1β Replace x→1t a(1t)2+b(1t)+c=0 In terms of variable x, a(1x)2+b(1x)+c=0 This is required equation.

If $α, β$ are the roots of the quadratic equation $a x^{2} + b x + c = 0, a \neq 0$ . Find the equation with roots $\frac{1}{α}$ and $\frac{1}{β} .$