First slide

Theory of equations

Question

If the roots $α, β, γ$ of the equation $x^{3} - 3 a x^{2} + 3 b x + c = 0$ are in H.P., then

Moderate

A

$β = \frac{1}{α}$
B

$β = b$
C

$β = \frac{c}{b}$
D

$\dot{β} = \frac{b}{c}$

Solution

Clearly, $\frac{1}{α}, \frac{1}{β}, \frac{1}{γ}$ are the roots of the equation
$- c x^{3} + 3 b x^{2} - 3 a x + 1 = 0$ and are in A.P
Now,
$\begin{array}{l} \frac{1}{α} + \frac{1}{β} + \frac{1}{γ} = \frac{3 b}{c} \\ \Rightarrow \frac{3}{β} = \frac{3 b}{c} \\ \Rightarrow β = \frac{c}{b} \end{array} [∵ \frac{1}{α} + \frac{1}{γ} = \frac{2}{β}$

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