## What is the Quadratic Formula?

### Algebra: Solve for x Help

#### Home | Solve for x menu | Algebra menu

If you have an equation

ax^{2}+bx+c = 0

the roots of the equation are found by the formula:

The expression b^{2} - 4ac is
called the discriminant . Its value tells
you whether you have no roots, 1 root or 2 roots.

**Case 1:** b^{2} - 4ac <0

If it is less than 0, that means you are trying to find the square root
of a negative number. Ergo, no roots. An example is
x^{2}-2x+5 .

**Case 2:** b^{2} - 4ac = 0

The square root of 0 is 0. One root. Period. An example is
x^{2}-2x+1 . The only root is
x = 1 .

**Case 2:** b^{2} - 4ac > 0

Here we have 2 roots. An example is
2x^{2}-x-15 . We have
a = 2 , b = -1 and
c = -15 . Plugging these numbers into the
formula, one root is 3 and the other is -5/2.

## Algebra: Solve for x Help

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