Find the discriminant, describe the types of roots, and find the solution for 3x^2-24x+12

The discriminant of a polynomial is given by:

b ^ 2-4ac

Substituting the values we have:

(-24) ^ 2-4 * (3) * (12) = 432

Since the discriminator is greater than zero, then the roots are real.

x = ( - b + / - root (b ^ 2-4ac)) / (2a)

Substituting the values:

x = ( - ( - 24) + / - root (432) / (2 * (3))

x = ( - ( - 24) + / - root (432) / (2 * (3))

x = ( - ( - 24) + / - root (144 * 3) / (2 * (3))

x = (24 + / - 12raiz (3) / (6)

x = 4 + / - 2raiz (3)

The roots are:

x1 = 4 + 2raiz (3)

x2 = 4 - 2raiz (3)

Answer:

432

the roots are real.

x1 = 4 + 2raiz (3)

x2 = 4 - 2raiz (3)