Find the quadratic equation whose roots are 2 and 3

To find the equation with roots of 2 and 3, we can simply multiply the factors together to find the original equation.

(x - 2) (x - 3)

FOIL.

x^2 - 3x - 2x + 6

Combine like terms.

x^2 - 5x + 6 is the new equation that has roots at 2 and 3.