Suppose that a polynomial function of degree 5 with rational coefficients has 0 (with multiplicity 2), 3, and 1 –2i as zeros. Find the remaining zero.

A. –2
B. –1 – 2i
C. 0
D. 1 + 2i

1. 1
1. So the funtion is:
x^2(x - 7)(x + 3 - 5i)(x - 3 + 5i)

For it to have rational coefficients, you must get rid of the -3 + 5i term.

Therefore the remaining zero is:
3 - 5i

posted by DD
2. How can the answer be 0 ? I don't get it, I figured to be -1-2i Choice B. What did i do wrong? Thanks!

posted by Jacinta
3. There is a little rule of thumb that you can count on for finding zeroes of polynomials with complex roots.
Complex roots always come in pairs. Each root of the pair is the complex conjugate of the other.
For example, if you have a root as 4+3i, the other root must be 4-3i. If another complex root is -2-i, then its conjugate is -2+i, etc.
To get the correct answer to the given problem, you only need to choose the complex conjugate of the given complex root.

posted by MathMate
4. The function would be
f(x)=x²(x-3)(x-1+2i)(x-1-2i)
= x5-5x4+11x³-15x²

posted by MathMate
5. 7+what equal 125

posted by kimora

## Similar Questions

1. ### Algebra

Suppose that a polynomial function of degree 5 with rational coefficients has 0 (with multiplicity 2), 6, and –2 + 3i as zeros. Find the remaining zero. A. –6 B. –2 – 3i C. 0 D. 2 + 3i
2. ### Precalculus

Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed. 2(multiplicity 2), -4(multiplicity 3)
3. ### Precalculus

Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed. 3(multiplicity 2), 5+i(multiplicity 1)
4. ### 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^3-2x^2+7x+6. 3)Find
5. ### PreCalculus

Suppose that a polynomial function of degree 5 with rational coefficients has the given numbers as zeros. Find the other zero( s): -1, radical 3, 11/3
6. ### Math

Write a polynomial of the lowest degree with real coefficients and with zeros 6-3i (multiplicity 1) and 0 ( multiplicity 5)
7. ### Algebra

Please help. Having a hard time with this. Find all of the zeros of the polynomial function and state the multiplicity of each. f (x) = (x^2 – 16)^2 A. – 4 with multiplicity 2 and 4 with multiplicity 2 B. – 4i with