Question

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

Answer 1

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)