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