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

$1$

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$m^{2}$

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$0$

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$m$

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Solution

The correct option is B
$m^{2}$

Given: $2 x^{2} - 2 (m^{2} + 1) x + (m^{4} + m^{2} + 1) = 0$

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

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

Using $α^{2} + β^{2}$ = $(α + β)^{2} - 2 α β$
From $(i) and (i i),$
$\Rightarrow α^{2} + β^{2} = (m^{2} + 1)^{2} - 2 \frac{(m^{4} + m^{2} + 1)}{2}$
$\Rightarrow α^{2} + β^{2} = m^{4} + 2 m^{2} + 1 - m^{4} - m^{2} - 1 = m^{2}$

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