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 - 5)^{2} = 1 5^{2} 2 a^{2} - 10 a - 200 = 0 2 . . . prime number 10 = 2 \cdot 5 200 = 2^{3} \cdot 5^{2} GCD (2, 10, 200) = 2 = 2 a^{2} - 5 a - 100 = 0 p = 1; q = - 5; r = - 100 D = q^{2} - 4 p r = 5^{2} - 4 \cdot 1 \cdot (- 100) = 425 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{5 \pm 4 2 5}{2} = \frac{5 \pm 5 1 7}{2} a_{1, 2} = 2.5 \pm 10.307764 a_{1} = 12.807764064 a_{2} = - 7.807764064 Factored form of the equation: (a - 12.807764064) (a + 7.807764064) = 0

Solution in text:

2a²-10a-200=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 1700
D > 0 ... The equation has two distinct real roots

a₁ = 12.8077641
a₂ = -7.8077641

P = {12.8077641; -7.8077641}