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:

(m - 1)^{2} = (m - 2)^{2} + (m - 3)^{2} - m^{2} + 8 m - 12 = 0 m^{2} - 8 m + 12 = 0 a = 1; b = - 8; c = 12 D = b^{2} - 4 a c = 8^{2} - 4 \cdot 1 \cdot 12 = 16 D > 0 m_{1, 2} = \frac{- b \pm D}{2 a} = \frac{8 \pm 1 6}{2} m_{1, 2} = \frac{8 \pm 4}{2} m_{1, 2} = 4 \pm 2 m_{1} = 6 m_{2} = 2 Factored form of the equation: (m - 6) (m - 2) = 0

Solution in text:

-m²+8m-12=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 16
D > 0 ... The equation has two distinct real roots

m₁ = 6
m₂ = 2

P = {6; 2}