For the equation 2x^2 - 2(m^2 + 1)x + m^4 + m | vedclass

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(D) For a quadratic equation $ax^2 + bx + c = 0$,the sum of roots $\alpha + \beta = -b/a$ and the product of roots $\alpha\beta = c/a$.Given the equat

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$m^2$

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(D) For a quadratic equation $ax^2 + bx + c = 0$,the sum of roots $\alpha + \beta = -b/a$ and the product of roots $\alpha\beta = c/a$.Given the equation $2x^2 - 2(m^2 + 1)x + (m^4 + m^2 + 1) = 0$:Sum of roots $\alpha + \beta = \frac{2(m^2 + 1)}{2} = m^2 + 1$.Product of roots $\alpha\beta = \frac{m^4 + m^2 + 1}{2}$.We know that $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta$.Substituting the values:$\alpha^2 + \beta^2 = (m^2 + 1)^2 - 2 	imes \frac{m^4 + m^2 + 1}{2}$.$\alpha^2 + \beta^2 = (m^4 + 2m^2 + 1) - (m^4 + m^2 + 1)$.$\alpha^2 + \beta^2 = m^2$.

For the equation $2x^2 - 2(m^2 + 1)x + m^4 + m^2 + 1 = 0$,if $\alpha$ and $\beta$ are the roots,then $\alpha^2 + \beta^2 = \dots$

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