For any quadratic polynomial equation of the form:



If your equation is not in standard form, fix it before you start.

Find the Discriminant, and evaluate the nature of the roots as follows:

No calculation quick look: If the signs on and are opposite, then guaranteed.

Two real and unequal roots. If is a perfect square, the quadratic factors over (the rationals).

One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors. Presuming rational coefficients, the root will be rational as well.

A conjugate pair of complex roots of the form where is the imaginary number defined by

John

My calculator said it, I believe it, that settles it

25 + 4x² = -20x
                    discriminant
how do you find the... (answered by solver91311,Edwin McCravy)

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The value of the discriminant for the equation below is 33.
2x^2+5x-1=0
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Let's put an equation with that curve. Use y = x2-8x+7

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