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Quadratic Discriminant

This one number can tell you whether the solutions to a quadratic equation are real or non-real, and whether they are distinct or repeated.

Quadratic Discriminant Warmup

         

If \(a = 2, b = 4, \text{ and } c = 1,\) what is the value of \(b^2 - 4ac?\)

If \(a = -2, b = 3, \text{ and } c = -1,\) what is the value of \(b^2 - 4ac?\)

When solving with the quadratic formula, Scott gets \(\sqrt{16 - 28}\) as part of his solution. The solutions will be:

A quadratic equation has a positive discriminant when set equal to zero. How many \(x\)-intercepts will the graph have?

What could be the value of \(b\) so that a quadratic equation with a discriminant of \(b^2 - 4(1)(2)\) has two real solutions?

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