Theory - Polynomial Equations, 2

Category: Algebra

"Published in Newark, California, USA"

Form the equation with the following roots:

Solution:

Since there are three given roots, then the degree of a polynomial must be a third degree but in this case, two of the roots have irrational numbers or radicals, then the degree of a polynomial will not be a third degree.

If the first root is -5, then the factor of a polynomial is (x + 5).

If the next root is 2 + √3 , then we need it's conjugate which is 2 - √3. Therefore, the factors of a polynomial are (x - 2 - √3) and (x - 2 + √3).

If the last root is 1 + √2, then we need it's conjugate which is 1 - √2. Therefore, the factors of a polynomial are (x - 1 - √2) and (x - 1 + √2). 

Therefore, the equation of a polynomial will be equal to