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:

1 0^{2} = (10 - 2 d)^{2} + (10 - d)^{2} - 5 d^{2} + 60 d - 100 = 0 5 d^{2} - 60 d + 100 = 0 5 . . . prime number 60 = 2^{2} \cdot 3 \cdot 5 100 = 2^{2} \cdot 5^{2} GCD (5, 60, 100) = 5 = 5 d^{2} - 12 d + 20 = 0 a = 1; b = - 12; c = 20 D = b^{2} - 4 a c = 1 2^{2} - 4 \cdot 1 \cdot 20 = 64 D > 0 d_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 2 \pm 6 4}{2} d_{1, 2} = \frac{1 2 \pm 8}{2} d_{1, 2} = 6 \pm 4 d_{1} = 10 d_{2} = 2 Factored form of the equation: (d - 10) (d - 2) = 0

Solution in text:

-5d²+60d-100=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 1600
D > 0 ... The equation has two distinct real roots

d₁ = 10
d₂ = 2

P = {10; 2}