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