Question

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

Answer 1

`{2, 3, pm i sqrt 5}`

Explanation:

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

We found 2 and 3.

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

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

`x^2 = -5`

`x = pm i sqrt 5`