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Quadratic equation
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===Quadratic factorization=== The term <math display="block">x - r</math> is a factor of the polynomial <math display="block">ax^2+bx+c</math> if and only if {{math|''r''}} is a [[root of a function|root]] of the quadratic equation <math display="block">ax^2+bx+c=0.</math> It follows from the quadratic formula that <math display="block">ax^2+bx+c = a \left( x - \frac{-b + \sqrt {b^2-4ac}}{2a} \right) \left( x - \frac{-b - \sqrt {b^2-4ac}}{2a} \right).</math> In the special case {{math|''b''<sup>2</sup> {{=}} 4''ac''}} where the quadratic has only one distinct root (''i.e.'' the discriminant is zero), the quadratic polynomial can be [[Factorization|factored]] as <math display="block">ax^2+bx+c = a \left( x + \frac{b}{2a} \right)^2.</math>
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