Algebra 2
posted by Anonymous .
Given that the polynomial has the given root, find all roots of the polynomial.
P(x) = x^4  5x^3 + 7x^2  5x + 6; i

well, if one root is i, it has another root +i, as complex roots will appear in conjugates. (x+i)(xi)=(x^2+1) is a factor. So, divide that into the polynomial....
(x^45x^3+7x^25x+6)/(x^2+1)=
x^25x+6=(x3)(x2)
so the roots are i, i, 3,2
Respond to this Question
Similar Questions

Algebra
Can someone please explain how to do these problems. 1)write a polynomial function of least degree with intregal coefficients whose zeros include 4 and 2i. 2)list all of the possible rational zeros of f(x)= 3x^32x^2+7x+6. 3)Find all … 
Math
Consider the polynomial f(x) = 2x^3 – 3x^2 – 8x – 3. (a) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial. (b) Find all of the zeros of the given polynomial. Be sure to show work, explaining … 
Algebra
Consider the polynomial: f(x) = 2x^3 – 3x^2 – 8x – 3. (a) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial. (b) Find all of the zeros of the given polynomial. Be sure to show work, … 
Math urgent
Find a degree 6 polynomial with  8 as a root, no other roots, and in which the coefficient of x^6 is 16. Assume that all (nonconstant) factors of the polynomial correspond to real zeroes. 
math 111 urgent please help
Find a degree 6 polynomial with  8 as a root, no other roots, and in which the coefficient of x^6 is 16. Assume that all (nonconstant) factors of the polynomial correspond to real zeroes. 
algebra
Consider the polynomial f(x) = 3x3 – 2x2 – 7x – 2. (a) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial. (b) Find all of the zeros of the given polynomial. Be sure to show work, explaining … 
algebra
Consider the polynomial f(x) = 3x3 – 2x2 – 7x – 2. (a) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial. (b) Find all of the zeros of the given polynomial. Be sure to show work, explaining … 
Algebra
Consider the polynomial f(x) = 3x3 – 2x2 – 7x – 2. (a) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial. (b) Find all of the zeros of the given polynomial. Be sure to show work, explaining … 
AlgebraVERY IMPORTANT
Given the polynomial x^2+10x+k Find all the values of k so that this given polynomial is factorable 
Algebra 2
How would you write a polynomial function with rational coefficients so that P(x)=0 has the given roots?