Multi-Module Assignment: Roots of Polynomials

Due at the end of Module 5

1. Counting multiple roots separately, how many roots do the following polynomials have?

a) f(x) = x4 – x3 + 5×2 – x + 1

b) f(x) = (x + 1)2 (x – 3)3

c) f(x) = x2 + 1

2. Find the nth degree polynomial function with real coefficients satisfying the given conditions. Use Desmos to check your solution.

n = 3; 4 and 2i are zeros; f(-1) = 50.

3. Using Desmos, find the roots of the following functions, and then write the function in factored form.

a) f(x) = x4 +10×3 +35×2 +50x + 24

b) f(x) = x3 +12×2 + 21x + 10

4. Using Desmos, determine the solutions to the following inequalities and write them in interval notation.

a) x2 + 3x < 0 b) x4 – 3x2 + x > 0