First slide

Theory of expressions

Question

The condition that one root of the equation $a x^{2} + b x + c = 0$ may be double of the other, is

Moderate

A

$b^{2} = 9 a c$
B

$2 b^{2} = 9 a c$
C

$2 b^{2} = a c$
D

$b^{2} = a c$

Solution

let the roots be $a$ and $2 a$ . Then,
$3 α = - \frac{b}{a}$ and $2 α^{2} = \frac{c}{a}$
$\Rightarrow α = - \frac{b}{3 a}$ and $α^{2} = \frac{c}{2 a} \Rightarrow {(- \frac{b}{3 a})}^{2} = \frac{c}{2 a} \Rightarrow 2 b^{2} = 9 a c$

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