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:

a^{2} + (17 - a)^{2} = 1 3^{2} 2 a^{2} - 34 a + 120 = 0 2 . . . prime number 34 = 2 \cdot 17 120 = 2^{3} \cdot 3 \cdot 5 GCD (2, 34, 120) = 2 = 2 a^{2} - 17 a + 60 = 0 p = 1; q = - 17; r = 60 D = q^{2} - 4 p r = 1 7^{2} - 4 \cdot 1 \cdot 60 = 49 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 7 \pm 4 9}{2} a_{1, 2} = \frac{1 7 \pm 7}{2} a_{1, 2} = 8.5 \pm 3.5 a_{1} = 12 a_{2} = 5 Factored form of the equation: (a - 12) (a - 5) = 0

Solution in text:

2a²-34a+120=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 196
D > 0 ... The equation has two distinct real roots

a₁ = 12
a₂ = 5

P = {12; 5}