# How do I use a graphing calculator to find the roots of the polynomial equation x^4-5x^3+11x^2-25x+30=0?

Jul 4, 2018

$\left\{2 , 3 , \pm i \sqrt{5}\right\}$

#### Explanation:

graph{x^4 - 5x^3 + 11x^2 - 25x + 30 [-1, 4, -4, 3]}

We found 2 and 3.

$\frac{{x}^{4} - 5 {x}^{3} + 11 {x}^{2} - 25 x + 30}{x - 2} = {x}^{3} - 3 {x}^{2} + 5 x - 15$

$\frac{{x}^{3} - 3 {x}^{2} + 5 x - 15}{x - 3} = {x}^{2} + 5 = 0$

${x}^{2} = - 5$

$x = \pm i \sqrt{5}$