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 is the expression . 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.
Showing a random 20 of 50 problems.
Example 1
hardFind all for which the line intersects in exactly one point.
Example 2
easyFind the discriminant of .
Example 3
easyHow many real solutions when ?
Example 4
mediumThe equation โ how many distinct real roots?
Example 5
mediumFind the discriminant of .
Example 6
mediumUse the discriminant to decide whether has two real solutions.
Example 7
mediumFor what values of does have two distinct real solutions?
Example 8
hardA parabola is tangent to the -axis. Find .
Example 9
mediumWithout solving, are the roots of real and rational?
Example 10
hardThe quadratic has roots whose sum is and product is . Use Vieta to find , then find the discriminant.
Example 11
mediumFor what value of does have exactly one real solution ()?
Example 12
challengeFind all for which has a repeated root.
Example 13
easyFind the discriminant of .
Example 14
mediumFind the discriminant of .
Example 15
easyFind the discriminant of .
Example 16
easyFind the discriminant of .
Example 17
mediumFor what values of does have no real solutions?
Example 18
hardFor what values of does have real solutions?
Example 19
mediumFor what values of does have no real solutions?
Example 20
challengeProve that for any real , the equation has two distinct real roots and find them.