If $x = \frac{- b + \sqrt{b^{2} - 4 a c}}{2 a}$ ; 'c' as the subject of the formula is $c = - a x^{2} - b x$ ( Enter 1 if true or 0 otherwise)

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Solution

Given expression is:
$x = \frac{- b + \sqrt{b^{2} - 4 a c}}{2 a}$
$2 a x = - b + \sqrt{b^{2} - 4 a c}$
$2 a x + b = \sqrt{b^{2} - 4 a c}$
$(2 a x + b)^{2} = b^{2} - 4 a c$
$4 a^{2} x^{2} + 4 a b x + b^{2} = b^{2} - 4 a c$
$4 a^{2} x^{2} + 4 a b x = - 4 a c$
$4 a (a x^{2} + b x) = - 4 a c$
$∴ c = - a x^{2} - b x$

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If $x = \frac{- b + \sqrt{b^{2} - 4 a c}}{2 a}$ ; 'c' as the subject of the formula is $c = - a x^{2} - b x$ ( Enter 1 if true or 0 otherwise)