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 y^{2} - 8 y + 12 = 0 2 y^{2} - 8 y + 12 = 0 2 . . . prime number 8 = 2^{3} 12 = 2^{2} \cdot 3 GCD (2, 8, 12) = 2 = 2 y^{2} - 4 y + 6 = 0 a = 1; b = - 4; c = 6 D = b^{2} - 4 a c = 4^{2} - 4 \cdot 1 \cdot 6 = - 8 D < 0 y_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 \pm - 8}{2} = \frac{4 \pm 2 - 2}{2} y_{1, 2} = \frac{4 \pm 2 i 2}{2} y_{1, 2} = 2 \pm 1.414214 i y_{1} = 2 + 1.4142135623731 i y_{2} = 2 - 1.4142135623731 i Factored form of the equation: (y - 2 - 1.4142135623731 i) (y - 2 + 1.4142135623731 i) = 0

Solution in text:

2y²-8y+12=0 ... quadratic equation

Discriminant:
D = b² - 4ac = -32
D < 0 ... The equation has two distinct complex roots

y₁ = 2+1.4142136i
y₂ = 2-1.4142136i

P = {2+1.4142136i; 2-1.4142136i}