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} + 1 = 2.5 * x x^{2} - 2.5 x + 1 = 0 a = 1; b = - 2.5; c = 1 D = b^{2} - 4 a c = 2 . 5^{2} - 4 \cdot 1 \cdot 1 = 2.25 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{2 . 5 \pm 2 . 2 5}{2} x_{1, 2} = 1.25 \pm 0.75 x_{1} = 2 x_{2} = 0.5 Factored form of the equation: (x - 2) (x - 0.5) = 0

Solution in text:

x²-2.5x+1=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 2.25
D > 0 ... The equation has two distinct real roots

x₁ = 2
x₂ = 0.5

P = {2; 0.5}