construct the polynomial function

Algebra
Tutor: None Selected Time limit: 1 Day

Construct a polynomial function with the following properties: third degree , only real coefficients, -3 and 2 + I are two of the zeros, y-intercepts is -30. Please explain how to get the answer and what the answer is.

May 6th, 2015

Since all coefficients of the polynomial are real and one of the zeros is 2 + i, the polynomial must also have a conjugate zero 2 - i. The degree of the polynomial is 3, so it must have three zeros and can be written as 

P(x) = A(x - x_1)(x - x_2)(x - x_3) where A is a constant.

Write P(x) = A(x - (-3))(x - 2 - i)(x - 2 + i) = 

A(x + 3)(x - 2 - i)(x - 2 + i) =           use the formula (a - b)(a + b) = a^2 - b^2 where a = x - 2, b = i

A (x + 3)[(x - 2)^2 - i^2] =                 use i^2 = -1

A(x + 3) (x^2 - 4x + 4 + 1) = A(x + 3)(x^2 - 4x + 5)

To find the A, use the y-intercept P(0) = -30: P(0) = 3*5*A = - 30, and A = -2.

Thus, the polynomial is P(x) = -2(x + 3)(x^2 - 4x + 5) = -2(x^3 - 4x^2 + 5x + 3x^2 - 12x + 15) =

-2(x^3 - x^2 - 7x + 15) = -2x^3 + 2x^2 + 14x - 30 

May 6th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
May 6th, 2015
...
May 6th, 2015
Feb 20th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer