1. Complete questions 1.a. and 2.a. on page 147 of the textbook. Answer
2. Solve the polynomial equation 2x3 − 5x2 − x + 10 = 4 algebraically. Answer

You will need to remember the following definitions in order to complete Try This 4.

 

zeros of a polynomial: values of the variable that make the polynomial equal to zero; for example, the zeros of the polynomial p(x) = (x − 1)(x + 2) are x = 1 and x = −2

 

roots of an equation: values of the variable that make the left side of the equation equal to the right side of the equation

In this module you worked with polynomials in expanded and factored form, polynomial equations, and graphs of polynomial functions. In Try This 4 and Share 3 you will investigate relationships among zeros, roots, and x-intercepts.

Try This 4

Refer to question 2 of Self-Check 2 to answer the following questions.

1. How is the original equation 2x3 − 5x2 − x + 10 = 4 from question 2 of Self-Check 2 related to the equation 2x3 − 5x2 − x + 6 = 0?
2. Using technology, graph f(x) = 2x3 − 5x2 − x + 6. How are the x-intercepts of the graph of f(x) = 2x3 − 5x2 − x + 6 related to the roots of the equation?
3. How are the roots of the equation related to the zeros of the polynomial p(x) = 2x3 − 5x2 − x + 6?

Save your responses in your course folder.

Share 3

With a partner or in a group, summarize the relationship between the zeros of the polynomial, the roots of the equation, and the x-intercepts of the graph of the polynomial.

If required, save a summary of your discussion in your course folder.