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:

2 r^{2} = (1 - r)^{2} r^{2} + 2 r - 1 = 0 a = 1; b = 2; c = - 1 D = b^{2} - 4 a c = 2^{2} - 4 \cdot 1 \cdot (- 1) = 8 D > 0 r_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 2 \pm 8}{2} = \frac{- 2 \pm 2 2}{2} r_{1, 2} = - 1 \pm 1.414214 r_{1} = 0.414213562 r_{2} = - 2.414213562 Factored form of the equation: (r - 0.414213562) (r + 2.414213562) = 0

Solution in text:

r²+2r-1=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 8
D > 0 ... The equation has two distinct real roots

r₁ = 0.4142136
r₂ = -2.4142136

P = {0.4142136; -2.4142136}