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 3^{2} = (- 3 - 2)^{2} + (- 5 - k)^{2} - k^{2} - 10 k + 119 = 0 k^{2} + 10 k - 119 = 0 a = 1; b = 10; c = - 119 D = b^{2} - 4 a c = 1 0^{2} - 4 \cdot 1 \cdot (- 119) = 576 D > 0 k_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 1 0 \pm 5 7 6}{2} k_{1, 2} = \frac{- 1 0 \pm 2 4}{2} k_{1, 2} = - 5 \pm 12 k_{1} = 7 k_{2} = - 17 Factored form of the equation: (k - 7) (k + 17) = 0

Solution in text:

-k²-10k+119=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 576
D > 0 ... The equation has two distinct real roots

k₁ = 7
k₂ = -17

P = {7; -17}