Question

You can use the what of a quadratic equation to determine the number and type of solutions of the equation?

Answer 1

You can use the determinant (square root) of a quadratic equation to determine the number and type of solutions of the equation.

$\sqrt{b^{2}-4ac}$ > 0    → 2 real solutions

• if $\sqrt{b^{2}-4ac}$ is a perfect square, then rational sol'ns

• if $\sqrt{b^{2}-4ac}$ is not a perfect square, then irrational sol'ns

$\sqrt{b^{2}-4ac}$ = 0    → 1 real solution (double root)

$\sqrt{b^{2}-4ac}$ < 0    → 2 imaginary(complex) solutions