Question

If α,β be the roots of the equation then ${\alpha }^2+{\beta }^2$=

• A. 0
• B. 1
• C. m
• D.

Answer 1

The correct option is D

α + β = $\frac{2(m^2+1)}{2}=m^2+1$ ......(i)

and αβ = $\frac{m^4+m^2+1}{2}$ .....(ii)

Therefore ${\alpha }^2+{\beta }^2$ = $(\alpha +\beta {)}^2-2\alpha \beta$

$=(m^2+1{)}^2-2\frac{(m^4+m^2+1)}{2}$

$=m^4+2m^2+1-m^4-m^2-1=m^2$