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:

3 x * (x - 4) + 10 = x * x 2 x^{2} - 12 x + 10 = 0 2 . . . prime number 12 = 2^{2} \cdot 3 10 = 2 \cdot 5 GCD (2, 12, 10) = 2 = 2 x^{2} - 6 x + 5 = 0 a = 1; b = - 6; c = 5 D = b^{2} - 4 a c = 6^{2} - 4 \cdot 1 \cdot 5 = 16 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{6 \pm 1 6}{2} x_{1, 2} = \frac{6 \pm 4}{2} x_{1, 2} = 3 \pm 2 x_{1} = 5 x_{2} = 1 Factored form of the equation: (x - 5) (x - 1) = 0

Solution in text:

2x²-12x+10=0 ... quadratic equation

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

x₁ = 5
x₂ = 1

P = {5; 1}