If $α, β$ are the roots of the equation $a x^{2} + b x + c = 0$ , find the value of $α^{2} + β^{2}$

\frac{b^{2} + 4 a c}{4 a}

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\frac{4 a c - b^{2}}{2 a}

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\frac{b^{2} - 2 a c}{a^{2}}

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\frac{b^{2} - 4 a c}{a^{2}}

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Solution

The correct option is C $\frac{b^{2} - 2 a c}{a^{2}}$
$a x^{2} + b x + c = 0 \Rightarrow α + β = \frac{- b}{a}$
& $α β = \frac{c}{a}$
As $α^{2} + β^{2} = (α + β)^{2} - 2 α β$
$\Rightarrow α^{2} + β^{2} = {(\frac{- b}{a})}^{2} - 2 \frac{c}{a}$
$α^{2} + β^{2} = \frac{b^{2} - 2 a c}{a^{2}}$

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