Quadratic equation calculator

Quadratic equation has the basic form:

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

Enter the quadratic equation's coefficients a, b, and c of its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant.

Calculation:

x^{2} + 3 + 1 x = 5 x x^{2} - 4 x + 3 = 0 a = 1; b = - 4; c = 3 D = b^{2} - 4 a c = 4^{2} - 4 \cdot 1 \cdot 3 = 4 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 \pm 4}{2} x_{1, 2} = \frac{4 \pm 2}{2} x_{1, 2} = 2 \pm 1 x_{1} = 3 x_{2} = 1 Factored form of the equation: (x - 3) (x - 1) = 0

Solution in text:

x²-4x+3=0 ... quadratic equation

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

x₁ = 3
x₂ = 1

P = {3; 1}