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MathML: Deriving the Quadratic Formula

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本页概述了二次方程式的推导

We take a quadratic equation in its general form, and solve for x:

a x 2 + b x + c = 0 a x 2 + b x = - c x 2 + b a x = -c a Divide out leading coefficient. x 2 + b a x + b 2 a 2 = - c ( 4 a ) a ( 4 a ) + b 2 4 a 2 Complete the square. ( x + b 2 a ) ( x + b 2 a ) = b 2 - 4 a c 4 a 2 Discriminant revealed. ( x + b 2 a ) 2 = b 2 - 4 a c 4 a 2 x + b 2 a = b 2 - 4 a c 4 a 2 x = -b 2 a ±{C} b 2 - 4 a c 4 a 2 There's the vertex formula. x = - b ±{C} b 2 - 4 a c 2 a

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