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:

q * 112 / 2 / 4^{2} = 1 + q^{2} + q - q^{2} + 2.5 q - 1 = 0 q^{2} - 2.5 q + 1 = 0 a = 1; b = - 2.5; c = 1 D = b^{2} - 4 a c = 2 . 5^{2} - 4 \cdot 1 \cdot 1 = 2.25 D > 0 q_{1, 2} = \frac{- b \pm D}{2 a} = \frac{2 . 5 \pm 2 . 2 5}{2} q_{1, 2} = 1.25 \pm 0.75 q_{1} = 2 q_{2} = 0.5 Factored form of the equation: (q - 2) (q - 0.5) = 0

Solution in text:

-q²+2.5q-1=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 2.25
D > 0 ... The equation has two distinct real roots

q₁ = 2
q₂ = 0.5

P = {2; 0.5}