Quadratic Equation Calculator

A quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the coefficients a, b, and c of the quadratic equation in its basic standardized form. The solution of a quadratic equation usually consists of two distinct real or complex roots, or one double root — calculated using the discriminant.

Calculation:

- x^{2} + 2 x + 3 = 3 - x^{2} + 2 x = 0 x^{2} - 2 x = 0 a = 1; b = - 2; c = 0 D = b^{2} - 4 a c = 2^{2} - 4 \cdot 1 \cdot 0 = 4 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{2 \pm 4}{2} x_{1, 2} = \frac{2 \pm 2}{2} x_{1, 2} = 1 \pm 1 x_{1} = 2 x_{2} = 0 Factored form of the equation: (x - 2) x = 0

Solution in text:

-x²+2x=0 ... c=0; quadratic equation without constant term

Discriminant:
D = b² - 4ac = 4
D > 0 ... The equation has two distinct real roots

x₁ = 2
x₂ = 0

P = {2; 0}