First slide

Theory of equations

Question

Suppose $α, β$ are roots of $a x^{2} + b x + c = 0$
then roots of $a (x - 2)^{2} - b (x - 2) (x - 3) + c (x - 3)^{2} = 0$ are

Moderate

A

$\frac{2 + α}{1 + β}, \frac{2 + β}{1 + α}$
B

$\frac{2 + α}{3 + β}, \frac{3 + α}{2 + β}$
C

$\frac{2 + 3 α}{2 + α}, \frac{2 + 3 β}{2 + β}$
D

$\frac{2 + 3 α}{1 + α}, \frac{2 + 3 β}{1 + β}$

Solution

Write the equation as
$a {(- \frac{x - 2}{x - 3})}^{2} + b (- \frac{x - 2}{x - 3}) + c = 0$
Now, $- \frac{x - 2}{x - 3} = α, β$
$\Rightarrow x = \frac{2 + 3 α}{1 + α}, \frac{2 + 3 β}{1 + β}$

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