To write : A fourth-degree polynomial equation with integer coefficients.
The required equation is
Given information:
The polynomial equation has two irrational roots and two imaginary roots.
Explanation :
Let the roots of a fourth- degree polynomial equation be
The polynomial in factor form will be:
Let
So, if the irrational roots are square roots then the radicals will disappear by using the above pattern to get perfect square terms.
So, let the irrational roots be
Now,
Let
Let
A fourth- degree polynomial equation with integer coefficients that has two irrational roots and two imaginary roots is
Chapter 5 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education