Evaluating the discriminant, sum and product of roots, quadratic inequalities, quadratics of other forms.
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The discriminant of a quadratic is the term under the square root in the quadratic formula:
When ​Δ<0, the square root has a negative value inside, and so the quadratic has no real solutions.
When ​Δ=0, the square root is zero, and the ​±√Δ​ makes no difference, so there is only one real solution.
When ​Δ>0, ​√Δ​ is positive and so ​±√Δ​ yields two real roots.
In a quadratic ​ax2+bx+c, the roots ​α​ and ​β​ satisfy
A quadratic inequality is an inequality of the form
They can be solved by finding the roots of the quadratic and the concavity of the parabola.
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