Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

Math question! About polynomials...?

A degree 4 polynomial with integer coefficients has zeros -4-2 i and 1, with 1 a zero of multiplicity 2. If the coefficient of x^4 is 1,

then the polynomial is ___________

10 Answers

Relevance
  • Anonymous
    1 decade ago
    Best Answer

    The complex roots come in conjugate pairs. So the roots are

    -4-2i and -4+2i.

    The other roots are 1 and 1.

    So the polynomial would looks like

    (x-(-4-2i)) * (x-(-4+2i)) * (x-1)^2

    =x^4+6*x^3+5*x^2-32*x+20

  • 1 decade ago

    4

  • NBL
    Lv 6
    1 decade ago

    Well, since the coefficients of the polynomial are real numbers, then the root -4 - 2i, has its conjugate pair as a root also, i.e.

    -4 + 2i

    ((x - 1)^2)(x + 4+2i)(x + 4 - 2i)

    Multiply this out, and you will get a fourth degree polynomial with real integer coefficients.

    x^4 + 6x^3 + 5x^2 - 32x + 20

  • 1 decade ago

    if -4-2i is zero then -4+2i is a zero

    if x=1 is a double zero

    then

    your polynomials is

    (x-1)^2*((x+4)^2+4)=

    (x^2-2x+1)(x^2+8x+20)=

    x^4+6x^3+5x^2-32x+20

  • How do you think about the answers? You can sign in to vote the answer.
  • Anonymous
    1 decade ago

    First, you find all of the zeroes.

    (complex numbers have conjugates)

    (-4-2i), (-4+2i), (+1), (+1)

    Then, you make it into the factored form of the polynomial.

    (x+4-2i)(x+4+2i)(x-1)(x-1)=0

    Then you multiply it out.

    (x^2+8x+20)(x^2-2x+1)=0

    x^4+6x^3+5x^2-32x+20=0

  • 1 decade ago

    4 isn't a polynomial

  • 1 decade ago

    #'s are everlasting they never end and a polynomial is in the 4th power an on & on & on 00000000000000000

  • Mike
    Lv 5
    1 decade ago

    Do your own homework.

  • 1 decade ago

    the answer is: STOP CHEATING- do your homework on your own.

Still have questions? Get your answers by asking now.