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:

2 z^{2} + 3 z + 1 = 0 2 z^{2} + 3 z + 1 = 0 a = 2; b = 3; c = 1 D = b^{2} - 4 a c = 3^{2} - 4 \cdot 2 \cdot 1 = 1 D > 0 z_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 3 \pm 1}{4} z_{1, 2} = \frac{- 3 \pm 1}{4} z_{1, 2} = - 0.75 \pm 0.25 z_{1} = - 0.5 z_{2} = - 1 Factored form of the equation: 2 (z + 0.5) (z + 1) = 0

Solution in text:

2z²+3z+1=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 1
D > 0 ... The equation has two distinct real roots

z₁ = -0.5
z₂ = -1

P = {-0.5; -1}