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:

p o w (x - 1, 2) + p o w (x - 4, 2) = 5 2 x^{2} - 10 x + 12 = 0 2 . . . prime number 10 = 2 \cdot 5 12 = 2^{2} \cdot 3 GCD (2, 10, 12) = 2 = 2 x^{2} - 5 x + 6 = 0 a = 1; b = - 5; c = 6 D = b^{2} - 4 a c = 5^{2} - 4 \cdot 1 \cdot 6 = 1 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{5 \pm 1}{2} x_{1, 2} = \frac{5 \pm 1}{2} x_{1, 2} = 2.5 \pm 0.5 x_{1} = 3 x_{2} = 2 Factored form of the equation: (x - 3) (x - 2) = 0

Solution in text:

2x²-10x+12=0 ... quadratic equation

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

x₁ = 3
x₂ = 2

P = {3; 2}