Algebra

posted by .

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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra 2

    write a polynomial function of least degree with integral coefficients whose zeros include 4 and 2i
  2. 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, …
  3. 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 …
  4. Math - Possible or Potential rational zeros

    List all possible (or potential) rational zeros for the polynomial below. Find all real zeros of the polynomial below and factor completely over the real numbers. Please show all of your work. f(x) = x^4 - 7x^3 - 3x^2 + 19x + 14
  5. algebra

    List all possible rational zeros for the polynomial below. Find all real zeros and factor completely. Please show all your work. f(x) = 2x^4 + 19x^3 + 37x^2 - 55x - 75
  6. Rational Zeros

    List all possible rational zeros for the polynomial below. Find all real zeros of the polynomial and factor f(x)=2x^4+19x^3+37x^2-55x-75
  7. pre-ap Algebra 2

    write a polynomial function f of least degree that has the rational coefficients, a leading coefficient of 1, and the given zeros. Given zeros: -2,2,-1,3, sqrt 11
  8. Math Problem (please help)

    Find all the zeros of the function. When there is an extended list of possible rational zeros, use a graphing utility to graph the function in order to discard any rational zeros that are obviously not zeros of the function. (Enter …
  9. algebra

    Using the rational zeros theorem to find all zeros of a polynomial The function below has at least one rational zero. Use this fact to find all zeros of the function g(x)=5x©ù-28©ø-48x©÷-8x+7 if more than one zero, separate with …
  10. algebra

    Using the rational zeros theorem to find all zeros of a polynomial The function below has at least one rational zero. Use this fact to find all zeros of the function h(x)=7x^4-9x^3-41x^2+13x+6 if more than one zero, separate with commas. …

More Similar Questions