Question

x^4-16x^3+90x^2-111x+173

When I put this equation into the graphing calculator, I get a parabola. I'm not sure how to find the zeros. Can you help?

Answer 1

Actually, It is not a parabola, it is a W shape. I try to adjust my window and still can't see it on the screen ok. please help

Answer 2

You're right, it is a W-shape, and in this case, it is more like a flattened parabola. The curve never touched the x-axis, so there are no real roots. In other words, all four roots are complex.

Are you familiar with solving a quartic? and working with complex numbers?

Answer 3

No, I have never solved a quartic nor am I familiar with working with complex numbers. The only thing I have used is the rational roots theorem and that doesn't work here.

Does that mean it can't be solved on the graphing calculator? Is there any way for you to guide me in the right direction?

Answer 4

The zeroes of the polynomial function are complex, so the expression cannot be factorized with rational coefficients.

If you are interested in the complex roots, you can try the following link:
http://www.sosmath.com/algebra/factor/fac12/fac12.html

Otherwise, the graph tells you that there are no real roots.

If you want to try the quartic formula, first try it with an equation that gives real roots. Once you have mastered it, you can try it with the above equation.