# The discriminant of a quadratic equation is -5. Which answer describes the number and type of solutions of the equation: 1 complex solution 2 real solutions 2 complex solutions 1 real solution?

May 24, 2017

Your quadratic equation has $2$ complex solutions.

#### Explanation:

The discriminant of a quadratic equation can only give us information about an equation of the form:

$y = a {x}^{2} + b x + c$ or a parabola.

Because the highest degree of this polynomial is 2, it must have no more than 2 solutions.

The discriminant is simply the stuff underneath the square root symbol ($\pm \sqrt{\text{ }}$), but not the square root symbol itself.

$\pm \sqrt{{b}^{2} - 4 a c}$

If the discriminant, ${b}^{2} - 4 a c$, is less than zero (i.e., any negative number), then you would have a negative under a square root symbol. Negative values under square roots are complex solutions. The $\pm$ symbol indicates that there is both a $+$ solution and a $-$ solution.

Therefore, your quadratic equation must have $2$ complex solutions.