Discriminant Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium

For what values of

k

does

x^2 + kx + 9 = 0

have two distinct real solutions?

Solution

1
Need $\Delta > 0$ : $k^2 - 4(1)(9) > 0$ .
2
$k^2 > 36$ .
3
$|k| > 6$ , so $k > 6$ or $k < -6$ .

Answer

k > 6 \text{ or } k < -6

By analyzing the discriminant as a function of the parameter

k

, we can determine which parameter values produce the desired number of solutions.

About Discriminant

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is the expression $\Delta = b^2 - 4ac$ . It determines the number and nature of the solutions.

Learn more about Discriminant →

More Discriminant Examples

Example 1 easy

Find the discriminant of [formula] and determine the number of solutions.

Example 3 easy

Find the discriminant of [formula].

Example 4 medium

Without solving, how many real solutions does [formula] have?

← All Discriminant Examples Discriminant Concept

Related Concepts

Quadratic Formula Quadratic Standard Form Zeros of a Quadratic Complex Numbers