**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*) = *x*4 – *x*3 + 5*x*2 – *x* + 1

b) *f*(*x*) = (*x* + 1)2 (*x* – 3)3

c) *f*(*x*) = *x*2 + 1

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

*n* = 3; 4 and 2*i *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*) = *x*4 +10*x*3 +35*x*2 +50*x* + 24

b)* f*(*x*) = *x*3 +12*x*2 + 21*x* + 10

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

a) *x*2 + 3*x* < 0

b) *x*4 – 3*x*2 + *x* > 0

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