Incomplete Quadratic Equations

A quadratic equation is incomplete when one of its terms is missing. You can solve x² − 9 = 0 without the formula: x² = 9, so x = 3 or x = −3. You can solve x² − 5x = 0 by factorising: x · (x − 5) = 0, so x = 0 or x = 5.

What does this generator do?

On the easy level you solve equations like 3x² − 75 = 0 and x² − 7x = 0 with whole-number roots. On the medium level the roots are fractions (4x² − 25 = 0) and some equations have no solution. On the hard level you rearrange first, for example (x + 2)² = 9 or x(x − 4) = 2x.

How to use it

1) If the x term is missing, make x² the subject and take the square root — remember both signs ±. 2) If the constant is missing, take out x: a product is zero when at least one factor is zero. 3) If x² equals a negative number, there is no real solution. 4) The roots can go in any order.