Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. Give the expression in the standard form a + bi.
Degree 5; zeros: 2, 3, 4, i
what are the values for a and b

Question

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. Give the expression in the standard form a + bi. 
Degree 5; zeros: 2, 3, 4, i 
what are the values for a and b

directrix · Answer

Degree 5; zeros: 2, 3, 4, i 

If the polynomial is of degree 5, then it has 5 zeros by the Fundamental Theorem of Algebra.

Four roots (2, 3, 4, i) are given. Note that one of them is not real. That root is i.

i can be written in a + bi form as 0 + 1i. 

If a non-Real number such as a + bi is a root of a polynomial with real coefficients, the a-bi is also a root of the same polynomial. a + bi and a - bi are called conjugates.

The fifth root of this polynomial is the conjugate of the aforementioned given root that is not Real. 

What is that root in a + bi form?  Don't forget this: what are the values for a and b

@u0860867