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# Online calculator. Solving of quadratic equations.

A quadratic equation is a polynomial equation of the second degree. The general form is

a x
2 +
b x
+
c
= 0,

where
x
represents a variable or an unknown, and
a
,
b
, and
c
are constants with
a
≠ 0. (If
a
= 0, the equation is a linear equation.)

The discriminant determines the number of the roots. There are three cases:

∆ =
b
2 - 4
ac
.
• If the discriminant is positive (∆ > 0), then there are two distinct roots, both of which are real numbers.
• If the discriminant is zero (∆ = 0), then there is exactly one distinct real root, sometimes called a double root (
x
1 =
x
2).
• If the discriminant is negative (∆ < 0), then there are no real roots.

The roots are given by the quadratic formula
 x1,2 = -b ± √∆ 2a

If in your quadratic equation there are subtraction signs, before corresponding coefficient in the calculator it is necessary to put a sign a minus ("-"). For example:

x
2 - 4
x
- 5 = 0, coefficients 1, -4, -5.
If in your quadratic equation there are less than three summand, near to an absent coefficient in the calculator it is necessary to put a zero ("0"). For example:
x
2 - 4x = 0, coefficients 1, -4, 0.

x
2 +
x
+  = 0

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