Quadratic equation calculator

Quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the coefficients a, b, c of quadratic equation in 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:

h^{2} - 4 * h + 20 h^{2} - 4 h + 20 = 0 a = 1; b = - 4; c = 20 D = b^{2} - 4 a c = 4^{2} - 4 \cdot 1 \cdot 20 = - 64 D < 0 h_{1, 2} = \frac{- b \pm \sqrt{D}}{2 a} = \frac{4 \pm \sqrt{- 64}}{2} = \frac{4 \pm 8 \sqrt{- 1}}{2} h_{1, 2} = \frac{4 \pm 8 i}{2} h_{1, 2} = 2 \pm 4 i h_{1} = 2 + 4 i h_{2} = 2 - 4 i Factored form of the equation: (h - 2 - 4 i) (h - 2 + 4 i) = 0

Solution in text:

h²-4h+20=0 ... quadratic equation

Discriminant:
D = b² - 4ac = -64
D<0 ... The equation has two distinct complex roots

h₁ = 2+4i
h₂ = 2-4i

P = {2+4i; 2-4i}