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:

r^{2} = (r - 2)^{2} + ((r - 1) / 2)^{2} - 0.25 r^{2} + 4.5 r - 4.25 = 0 0.25 r^{2} - 4.5 r + 4.25 = 0 a = 0.25; b = - 4.5; c = 4.25 D = b^{2} - 4 a c = 4 . 5^{2} - 4 \cdot 0.25 \cdot 4.25 = 16 D > 0 r_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 . 5 \pm 1 6}{0 . 5} = 9 \pm 44 r_{1, 2} = 9 \pm 8 r_{1} = 17 r_{2} = 1 Factored form of the equation: 0.25 (r - 17) (r - 1) = 0

Solution in text:

-0.25r²+4.5r-4.25=0 ... quadratic equation

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

r₁ = 17
r₂ = 1

P = {17; 1}