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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