First slide

Theory of equations

Question

If $α, β$ be the roots of the equation
$2 x^{2} - 2 (m^{2} + 1) x + m^{4} + m^{2} + 1 = 0,$ then $α^{2} + β^{2} =$

Moderate

A

$0$
B

$1$
C

$m$
D

$m^{2}$

Solution

$α + β = \frac{2 (m^{2} + 1)}{2} = m^{2} + 1 . . . (i) and αβ = \frac{m^{4} + m^{2} + 1}{2} . . . (ii)$
Therefore $α^{2} + β^{2} = {(α + β)}^{2} - 2 αβ$
$= {(m^{2} + 1)}^{2} - 2 \frac{(m^{4} + m^{2} + 1}{2} = m^{4} + 2 m^{2} + 1 - m^{4} - m^{2} - 1 = m^{2}$

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