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:

3 (z^{2} - 16 z + 48) = 0 3 z^{2} - 48 z + 144 = 0 3 . . . prime number 48 = 2^{4} \cdot 3 144 = 2^{4} \cdot 3^{2} GCD (3, 48, 144) = 3 = 3 z^{2} - 16 z + 48 = 0 a = 1; b = - 16; c = 48 D = b^{2} - 4 a c = 1 6^{2} - 4 \cdot 1 \cdot 48 = 64 D > 0 z_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 6 \pm 6 4}{2} z_{1, 2} = \frac{1 6 \pm 8}{2} z_{1, 2} = 8 \pm 4 z_{1} = 12 z_{2} = 4 Factored form of the equation: (z - 12) (z - 4) = 0

Solution in text:

3z²-48z+144=0 ... quadratic equation

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

z₁ = 12
z₂ = 4

P = {12; 4}