Posted by **Marissa** on Friday, August 10, 2007 at 10:30pm.

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 all of the rational zeros of f(x)= 4x^3-3x^2-22x-15.

Because all the coefficients of the polynomial are real, if 2i is a zero, then the complex conjugate -2i must also be a zero. This means that the least order polynomial is proportional to:

(x-4)(x-4i)(x+4i)= (x-4)(x^2 + 16)=

x^3 - 4x^2 + 16 x - 64

To find the rational roots, use the Rational Roots Theorem: if x = p/q is a rational root (and p and q don't have any divisors in common), then p must divide the constant term and q the coefficient of the highest power of x.

In case of the polynomial

3x^3-2x^2+7x+6.

Ths means that p is a divisor of 6 and q a divisor of 3.

## Answer This Question

## Related Questions

- Algebra 2 - write a polynomial function of least degree with integral ...
- pre-ap Algebra 2 - write a polynomial function f of least degree that has the ...
- Math Problem (please help) - Find all the zeros of the function. When there is ...
- calculus--please help!! - I have two questions that I don't understand and need ...
- Rational Zeros - List all possible rational zeros for the polynomial below. Find...
- Precalculus - Suppose that a polynomial function of degree 4 with rational ...
- algebra - Using the rational zeros theorem to find all zeros of a polynomial The...
- Algebra - Consider the polynomial: f(x) = 2x^3 – 3x^2 – 8x – 3. (a) By using the...
- algebra - Using the rational zeros theorem to find all zeros of a polynomial The...
- Math - Possible or Potential rational zeros - List all possible (or potential) ...

More Related Questions