Algebra 2

posted by .

find all the zeros of the polynomial function
F(x)= x^4+4x^3-6x^2-36x-27

  • Algebra 2 -

    There are websites that solve such root-finding questions automatically, but they are not very instructive.

    If there are integer roots, they must be even divisors of 27: +/- 1, 3, 9 or 27.
    That is a consequence of the "rational roots theorem", which you should learn.

    One such root is -1, so x+1 is a factor.
    The other factor is
    (x^4+4x^3-6x^2-36x-27)/(x+1)
    = x^3 +3x^2 -9x -27
    (obtained with polynomial long division)
    x = 3 is clearly another root, so (x-3) is another factor. Divide the cubic by (x-3) and you get
    x^2 + 6x +9 = 0
    which can be factored to give
    (x+3)^2 = 0

    That means x = -3 is a double root.
    The roots are -3, +3 and -1

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Polynomiials

    Find a polynomial function with real coefficients that has the given numbers as roots: 4, 0, 3, italic i a)x^4-4x^3 +9x^2-36x b)x^3-4x^2 -3x+12 c)x^3-4x^2 +3x-12 d)4x-4x^3 -9x^2 +36x My gut instinct is either b or c but I could be …
  2. 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 all …
  3. algebra

    p(x)=x^3+2x^2-3x+20 one of this functions zeros is -4 When using synthetic division to find all the zeros of a polynomial function, would you plug in 4 or -4 into the actual equation?
  4. college algebra

    use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)=x^3-8x^2-31x-22
  5. College Algebra

    Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)=2x^3-x^2+2x-1
  6. Algebra

    Use the rational zeros theorem to list the potential reational zeros of the polynomial function. Do not attempt to find the zeros. f(x)=6x^4+9x^3+30x^2+63x+28
  7. College algebra

    Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers f(x)=9x^4+28x^3+66x^2+196x+21 Find the real zeros of f Use the real zeros to factor f f(x)=
  8. 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 …
  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 h(x)=7x^4-9x^3-41x^2+13x+6 if more than one zero, separate with commas. …
  10. algebra

    Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)= x^4+6x^3-11x^2-24x+28 Molon

More Similar Questions