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:

a^{2} + (a - 1)^{2} = 5^{2} 2 a^{2} - 2 a - 24 = 0 2 . . . prime number 24 = 2^{3} \cdot 3 GCD (2, 2, 24) = 2 = 2 a^{2} - a - 12 = 0 p = 1; q = - 1; r = - 12 D = q^{2} - 4 p r = 1^{2} - 4 \cdot 1 \cdot (- 12) = 49 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 \pm 4 9}{2} a_{1, 2} = \frac{1 \pm 7}{2} a_{1, 2} = 0.5 \pm 3.5 a_{1} = 4 a_{2} = - 3 Factored form of the equation: (a - 4) (a + 3) = 0

Solution in text:

2a²-2a-24=0 ... quadratic equation

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

a₁ = 4
a₂ = -3

P = {4; -3}