First slide

Theory of equations

Question

if $α, β$ are roots of the equation $x^{2} + x + 1 = 0,$ then the equation whose roots are $\frac{α}{β}$ and $\frac{β}{α}$ , is

Moderate

A

$x^{2} + x + 1 = 0$
B

$x^{2} - x + 1 = 0$
C

$x^{2} - x - 1 = 0$
D

$x^{2} + x - 1 = 0$

Solution

We have, $α = ω$ and $β = ω^{2}$
$∴ \frac{α}{β} = w^{2}$ and $\frac{β}{α} = w$
Hence, the equation having $\frac{α}{β}$ i.e. $ω^{2}$ and $\frac{β}{α}$ i.e $ω$ as its roots is $x^{2} + x + 1 = 0$ .

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