When a polynomial equation of second degree (quadratic equation) is given in the form

$ax2+\; bx\; +\; c\; =\; 0$then this page will find the up to 2 real or complex solutions
_{1}_{2}*roots*) via the quadratic formula

Enter the 3 coefficients `a`

, `b`

and `c`

.
This page will then find the up to 2 real or complex roots.

`1/4`

, not
`0.25`

)`5/3`

, not
`1 2/3`

)`-1/3`

, not `1/-3`

)Enter the 3 coefficients

With

The term underneath the root, ^{2} - 4ac*Discriminant*. Its value governs, how many solutions we get, and of what type these solutions are.

Plugging the discriminant back into the formula:

$-1/4nbspplusmnnbsp(1/4)i7676$Calculating the formula's simplest terms:

$-1/24nbspplusmnnbsp(1/24)i767$Hence the two solutions are:

$-1/24nbsp+nbsp(1/24)i767nbsp(decimal\; approx.\; -0.0416666666666667\; +\; 1.15394853534385$and

$-1/24nbsp-nbsp(1/24)i767nbsp(decimal\; approx.\; -0.0416666666666667\; -\; 1.15394853534385$