Polynomial functions questions?

1. Solve 3x^{3}-13x^{2}+19x-5 = 0 given that there are no integral nor negative roots.

2. The polynomial function y=x^{4}-11x^{3}+40x^{2}-55x+25. It intersects the x-axis at x=1, x=5, and at two other points.

Determine these other two x-intercepts.

Thanks!

Re: Polynomial functions questions?

Quote:

Originally Posted by

**WhatthePatel** 1. Solve 3x^{3}-13x^{2}+19x-5 = 0 given that there are no integral nor negative roots.

The rational root theorem says the only possible (positive, non-integral) roots are 1/3 and 5/3.

-Dan

Re: Polynomial functions questions?

Quote:

Originally Posted by

**WhatthePatel** 2. The polynomial function y=x^{4}-11x^{3}+40x^{2}-55x+25. It intersects the x-axis at x=1, x=5, and at two other points.

Determine these other two x-intercepts.

If we have a root at x = 1 then we know that the polynomial has a factor (x - 1). So you can divide (long hand or synthetic division) the polynomial to find that x ^4 - 11x^3 + 40x^2 - 55x + 25 = (x - 1)(x^3 - 10x^2 + 30x - 25)

So what can you do with the root at x = 5?

-Dan

Re: Polynomial functions questions?