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:

(100 - 2 p) * (100 - p) = 100 * (100 - 62.5) 2 p^{2} - 300 p + 6250 = 0 2 . . . prime number 300 = 2^{2} \cdot 3 \cdot 5^{2} 6250 = 2 \cdot 5^{5} GCD (2, 300, 6250) = 2 = 2 p^{2} - 150 p + 3125 = 0 a = 1; b = - 150; c = 3125 D = b^{2} - 4 a c = 15 0^{2} - 4 \cdot 1 \cdot 3125 = 10000 D > 0 p_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 5 0 \pm 1 0 0 0 0}{2} p_{1, 2} = \frac{1 5 0 \pm 1 0 0}{2} p_{1, 2} = 75 \pm 50 p_{1} = 125 p_{2} = 25 Factored form of the equation: (p - 125) (p - 25) = 0

Solution in text:

2p²-300p+6250=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 40000
D > 0 ... The equation has two distinct real roots

p₁ = 125
p₂ = 25

P = {125; 25}