Practice Quadratic Formula in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A formula giving the exact solutions to any quadratic equation directly from its three coefficients.
When factoring fails, this formula always finds the x-intercepts.
Showing a random 20 of 50 problems.
Example 1
mediumSolve .
Example 2
easySolve .
Example 3
mediumSolve . Leave answers in exact form.
Example 4
mediumSolve .
Example 5
challengeIf the roots of are in the ratio , find .
Example 6
mediumSolve .
Example 7
challengeFind all values of for which has two distinct positive real roots.
Example 8
easySolve .
Example 9
mediumA rectangular garden has area m² and its length is m more than its width. Find the width.
Example 10
easyFind the discriminant of and state how many real roots the equation has.
Example 11
mediumSolve .
Example 12
challengeProve that for any real , the equation has at least one real solution.
Example 13
easySolve .
Example 14
mediumSolve using the quadratic formula.
Example 15
hardA projectile follows metres. When does it reach height m? Give all solutions to two decimal places.
Example 16
hardFind values of such that has no real roots.
Example 17
easySolve using the quadratic formula.
Example 18
mediumSolve .
Example 19
hardSolve .
Example 20
mediumFind the values of for which has a double root.