Which correctly describes the roots of the following cubic equation x^3-5x^2+3x+9=0? A. Three real roots, each with a different value B. One real root and to complex roots C. Three real roots, two of which are equal in value D. 2 real roots and one complex root?

Question

Salem

Mathematics

5 August, 01:15

Which correctly describes the roots of the following cubic equation x^3-5x^2+3x+9=0? A. Three real roots, each with a different value B. One real root and to complex roots C. Three real roots, two of which are equal in value D. 2 real roots and one complex root?

+4

Answers (1)

Know the Answer?

Kaila Avila · Answer 1

The correct answer is letter C, because you have to calculate de discriminating which is 18abcd-4b^3d+b^2c^2-4ac^3-27a^2d^2 = 0

For your equation a=1, b=-5, c=3, d=9

So when the discriminating is equal zero, the equation has 3 real roots, two of which are equal in value.

You can prove this solving your equation using Ruffini's Rule and you will get the roots are: 3, 3, and - 1