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:

z^{2} + 1 2^{2} = 40 * z z^{2} - 40 z + 144 = 0 a = 1; b = - 40; c = 144 D = b^{2} - 4 a c = 4 0^{2} - 4 \cdot 1 \cdot 144 = 1024 D > 0 z_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 0 \pm 1 0 2 4}{2} z_{1, 2} = \frac{4 0 \pm 3 2}{2} z_{1, 2} = 20 \pm 16 z_{1} = 36 z_{2} = 4 Factored form of the equation: (z - 36) (z - 4) = 0

Solution in text:

z²-40z+144=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 1024
D > 0 ... The equation has two distinct real roots

z₁ = 36
z₂ = 4

P = {36; 4}