# Discriminants

The discriminant of a quadratic equation will tell you how many roots the quadratic equation has.

Solutions of a quadratic equation are known as roots; they can be seen on the graph of a quadratic where the graph crosses the x-axis. Recall that the general quadratic equation: $ax^2+bx+c=0$, can have two distinct roots, one repeated roots or no roots at all (unless you are working with complex numbers).

The discriminant can tell you how many roots a quadratic equation will have without having to actually find them.

For the quadratic equation $ax^2+bx+c=0$, the discriminant is given by $b^2-4ac$.

• If $b^2-4ac \hspace{2pt}\textgreater\hspace{2pt} 0$, the equation has two distinct roots.
• If $b^2-4ac = 0$, the equation has one repeated root.
• If $b^2-4ac\hspace{2pt}\textless\hspace{2pt}0$, the equation has no roots.

## Example 1

Given that the quadratic equation $kx^2-4x+2$ has equal roots, find the value of k.

## Example 2

A quadratic has equation $y=px^2+3px-5$.

1. Calculate the discriminant of the quadratic.
2. Given that the quadratic has two distinct roots, find the possible values of p.

## Past Discriminant Exam Questions

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## Solomon Practice Questions

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