Ask Question
15 December, 17:58

Find the third-degree polynomial function that has zeros - 2 and - 15i, and a value of 1,170 when x=3.

+1
Answers (1)
  1. 15 December, 19:44
    0
    The third degree polynomial function = x³ + 27x² + 200x + 300

    Step-by-step explanation:

    The third-degree polynomial function has zeros - 2 and - 15.

    From the above, we have been given two factors of the polynomial function. Let's derive the factors from the two zeros of the polynomial given.

    The two given zeros of the polynomial can be written as:

    x = - 2

    x+2 = 0

    (x+2) is a factor of the polynomial

    x = - 15

    x+15 = 0

    (x+15) is a factor of the polynomial

    So we have two factors of the polynomial (x+2) and (x+15). But since it is a third degree polynomial, we have to find the third factor.

    Let (x-b) be the third factor and f (x) represent the third degree polynomial

    f (x) = (x-b) (x+2) (x+15)

    Expanding (x+2) (x+15) = x² + 2x + 15x + 30

    (x+2) (x+15) = x² + 17x + 30

    f (x) = (x-b) (x² + 17x + 30)

    From the given information, a value of 1,170 is obtained when x=3

    f (3) = 1170

    Insert 3 for x in f (x)

    f (3) = (3-b) (3² + 17 (3) + 30)

    1170 = (3-b) (9 + 51 + 30)

    1170 = (3-b) (90)

    1170/90 = 3-b

    3-b = 13

    b = 3-13 = - 10

    Insert value of b in f (x)

    f (x) = [x - (-10) ] (x² + 17x + 30)

    f (x) = (x+10) (x² + 17x + 30)

    f (x) = x³ + 17x² + 30x + 10x² + 170x + 200x + 300

    f (x) = x³ + 27x² + 200x + 300

    The third degree polynomial function = x³ + 27x² + 200x + 300
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “Find the third-degree polynomial function that has zeros - 2 and - 15i, and a value of 1,170 when x=3. ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers