# Polynomial functions questions?

• Jan 15th 2013, 03:54 PM
WhatthePatel
Polynomial functions questions?
1. Solve 3x3-13x2+19x-5 = 0 given that there are no integral nor negative roots.
2. The polynomial function y=x4-11x3+40x2-55x+25. It intersects the x-axis at x=1, x=5, and at two other points.
Determine these other two x-intercepts.

Thanks!

• Jan 15th 2013, 04:08 PM
topsquark
Re: Polynomial functions questions?
Quote:

Originally Posted by WhatthePatel
1. Solve 3x3-13x2+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
• Jan 15th 2013, 04:12 PM
topsquark
Re: Polynomial functions questions?
Quote:

Originally Posted by WhatthePatel
2. The polynomial function y=x4-11x3+40x2-55x+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
• Jan 15th 2013, 04:43 PM
WhatthePatel
Re: Polynomial functions questions?
Thank you ^^