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Applications of Quadratics
Evaluating the discriminant, sum and product of roots, quadratic inequalities, quadratics of other forms.
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.
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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