Practice Discriminant in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

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.

The discriminant is the expression under the square root in the quadratic formula. If it is positive, you can take the square root and get two answers. If it is zero, the square root is zero so both answers are the same. If it is negative, you cannot take a real square root, so there are no real solutions.

Example 1

easy
Find the discriminant of x^2 - 6x + 9 = 0 and determine the number of solutions.

Example 2

medium
For what values of k does x^2 + kx + 9 = 0 have two distinct real solutions?

Example 3

easy
Find the discriminant of 2x^2 + 5x - 3 = 0.

Example 4

medium
Without solving, how many real solutions does 3x^2 + 2x + 5 = 0 have?