Editing Quadratic equation (section)

===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 {{math|''a''}}, which is always possible since {{math|''a''}} is non-zero.  This produces the ''reduced quadratic equation'':<ref>Alenit͡syn, Aleksandr and Butikov, Evgeniĭ. ''Concise Handbook of Mathematics and Physics'', p. 38 (CRC Press 1997)</ref>

<math display="block">x^2+px+q=0,</math>

where {{math|''p'' {{=}} ''b''/''a''}} and {{math|''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
<math display="block">x = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}\,.</math>