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:

c^{2} = (c - 1)^{2} + (c - 2)^{2} - c^{2} + 6 c - 5 = 0 c^{2} - 6 c + 5 = 0 p = 1; q = - 6; r = 5 D = q^{2} - 4 p r = 6^{2} - 4 \cdot 1 \cdot 5 = 16 D > 0 c_{1, 2} = \frac{- q \pm D}{2 p} = \frac{6 \pm 1 6}{2} c_{1, 2} = \frac{6 \pm 4}{2} c_{1, 2} = 3 \pm 2 c_{1} = 5 c_{2} = 1 Factored form of the equation: (c - 5) (c - 1) = 0

Solution in text:

-c²+6c-5=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 16
D > 0 ... The equation has two distinct real roots

c₁ = 5
c₂ = 1

P = {5; 1}