Graph fx x4 7x3 11x2 7x 10 What is the WINDOW you need

Graph f(x) = x^4 - 7x^3 + 11x^2 - 7x + 10 What is the WINDOW you need on your calculator to see all the maximum and minimum points? How many roots does f(x) have? How many are real? How many are imaginary? Find the root and the factors

Solution

f(x) = x^4 - 7x^3 + 11x^2 – 7x + 10

a) Needed window =====> x = -4 to x = 12

b) No. of roots = 4

No. of real roots = 2

No. of imaginary roots = 2

c) Factors ====> (x - 5)(x - 2)(x^2 + 4x + 5)

Roots ====> 5, 2, (-2 + i), (-2 - i)