SOLUTION: Find a 3rd degree polynomial with integral coefficients that has 2 +i and -3 as two of its roots.

Question 801325: Find a 3rd degree polynomial with integral coefficients that has 2 +i and -3 as two of its roots.
Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
Roots given ALSO include 2-i, the conjugate of 2+i.

Form the binomial factors of the polynomial based on the now known roots:
x+3, (x-(2+i)), (x-(2-i)).

Wanting only general form polynomial with integer coefficients, work with first the two complex factors with the imaginary components:

Recognize the factors giving the difference of two squares.

Still in factored form but showing only integer coefficients within each polynomial factor, polynomial is which you can further multiply if you need.
RELATED QUESTIONS
Write a polynomial equation with integral coefficients that has 0,1,2, and -3 as its... (answered by ikleyn)

Find a polynomial equation with integral coefficients and of lowest degree that has the... (answered by Boreal)

Find a polynomial equation with integral coefficients that has the roots: -2, 2,... (answered by solver91311,MEYDA,MathTherapy)

Find a third-degree polynomial equation with rational coefficients that has the given... (answered by erica65404)

f(x) is a 3rd Degree Polynomial Equation having Real coefficients, if it has 3, i and -i... (answered by nerdybill)

write a polynomial function of least degree with integral coefficients having roots (... (answered by josgarithmetic)

Find a polynomial with smallest degree with rational coefficients that has roots (2 -... (answered by t0hierry)

Write the polynomial with integral coefficients that has the given numbers as solutions... (answered by josgarithmetic)

Find the polynomial equation with integral coefficients that has the given roots: -2, i,... (answered by Edwin McCravy)