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

Mathematics

Cailyn Cohen

31 March, 04:49

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?

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Cash Little · 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