First slide

Theory of equations

Question

If the roots of the equation ${ax}^{2} - bx + c = 0 are α, β,$ the roots of the equation $b^{2} {cx}^{2} - {ab}^{2} x + a^{3} = 0$ are

Moderate

A

$\frac{1}{α^{3} + αβ}, \frac{1}{β^{3} + αβ}$
B

$\frac{1}{α^{2} + αβ}, \frac{1}{β^{2} + αβ}$
C

$\frac{1}{α^{4} + α β}, \frac{1}{β^{4} + α β}$
D

none of these

Solution

Multiplying the given equation by $c / a^{3},$ we get
$\frac{b^{2} c^{2}}{a^{3}} x^{2} - \frac{b^{2} c}{a^{2}} x + c = 0$
$\begin{array}{l} or a {(\frac{bc}{a^{2}} x)}^{2} - b (\frac{bc}{a^{2}}) x + c = 0 \\ \Rightarrow \frac{bc}{a^{2}} x = α, β \\ \Rightarrow (α + β) αβx = α, β \\ \Rightarrow x = \frac{1}{(α + β) α}, \frac{1}{(α + β) β} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App