Quadratic equation
Reduced quadratic equation

It is sometimes convenient to reduce a quadratic equation so that its leading coefficient is one. This is done by dividing both sides by a, which is always possible since a is non-zero. This produces the reduced quadratic equation:

x 2 + p x + q = 0, {\displaystyle x^{2}+px+q=0,}

where p = b / a and q = c / a. This monic polynomial equation has the same solutions as the original.

The quadratic formula for the solutions of the reduced quadratic equation, written in terms of its coefficients, is x = − p 2 ± (p 2) 2 − q. {\displaystyle x=-{\frac {p}{2}}\pm {\sqrt {\left({\frac {p}{2}}\right)^{2}-q}}\,.}
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