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Applications of Quadratics
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Evaluating the discriminant, sum and product of roots, quadratic inequalities, quadratics of other forms.
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The discriminant and solution count
SL AA 2.7
The discriminant of a quadratic is the term under the square root in the quadratic formula:
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Δ=b2−4ac📖
​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.
Quadratic Inequalities
SL AA 2.7
A quadratic inequality is an inequality of the form
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ax2+bx+c{<≤>≥}0
​They can be solved by finding the roots of the quadratic and the concavity of the parabola.
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