First slide

Theory of equations

Question

If $α, β, γ$ are the roots of the equation $2 x^{3} - 3 x^{2} + 6 x + 1 = 0, then α^{2} + β^{2} + γ^{2}$ is equal to

Moderate

A

$- \frac{15}{4}$
B

$\frac{15}{4}$
C

$\frac{9}{4}$
D

$4$

Solution

Given equation $2 x^{3} - 3 x^{2} + 6 x + 1 = 0$
$α + β + γ = \frac{3}{2}, αβγ = \frac{- 1}{2}, \sum_{} αβ = 3$
$(α^{2} + β^{2} + γ^{2}) = {(α + β + γ)}^{2} - 2 (\sum_{} αβ)$
$= {(\frac{3}{2})}^{2} - 2.3 = \frac{9}{4} - 6 = \frac{- 15}{4} .$

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