Question

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?

Answer 1

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=ax^2+bx+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 (`+-sqrt(" ")`), but not the square root symbol itself.

`+-sqrt(b^2-4ac)`

If the discriminant, `b^2-4ac`, 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 `+-` symbol indicates that there is both a `+` solution and a `-` solution.

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