Algebra II

Write the simplest polynomial function with the zeros 2-i, square root of 5, and -2.

I know that the conjugates are 2+i and -the square root of five, but when I multiply it comes out wrong.

not sure

A toy rocket is launched from the ground level with an initial vertical velocity of 96ft/s. After how many seconds will the rocket hit the ground?

In order to have your "simple polynomial function" I assume you want only rational coefficients.
For that to happen the zeros of 2-i and √5 must indeed have conjugate partner factors.
to get your given zeros included, the function must be
f(x) = (x-2-i)(x-2+i)(x^2 - 5)(x + 2)

I will leave the expansion up to you.
Hint: the first two factors expanded should have given you x^2 - 4x + 5

I don't usually work with non-metric units but I recall that the equation that would describe the height of this toy rocket would be
h = -16t^2 + 96t where t is seconds, and h is the height in feet

you want that height to be zero, so
0 = -16t^2 + 96t
16t^2 - 96t = 0
t(16t - 96)=0
so t=0 or t=6

the t=0 of course gives you the initial height, and
t=6 seconds would be the answer to your question.

Thank you so much for taking the time to help me with this problem. It was so nice of you!

I thought that how you told me is the way to set it up, but the mult. of the factors is what gives me trouble. In the answer, should there be square roots and "i"s? In your function I think you left out x^+5, is that right? I need more help!!)

  1. 👍 1
  2. 👎 0
  3. 👁 470
asked by K.

Respond to this Question

First Name

Your Response

Similar Questions

  1. Precalculus

    Suppose that a polynomial function of degree 4 with rational coefficients has i and (-3 + square root of 3)as zeros find the other zeros

    asked by Arielt on March 14, 2010
  2. Precalculus

    Suppose that a polynomial function of degree 4 with rational coefficients has i and (-3 + square root of 3)as zeros find the other zeros show work please

    asked by Arielt on March 14, 2010
  3. algebra

    how do you write the simplest polynomial function with the given zeros

    asked by john on December 4, 2014
  4. Algebra

    Write the simplest polynomial function with zeros five and -4. K(x) = x^2 - x - 20?

    asked by Anonymous on November 17, 2014
  5. 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

    asked by Marissa on August 10, 2007
  6. Trigonometry

    Write the quadratic function whose zeros are: 1. 2+square root of 5, 2-square root of 5 2. 3+7i,3-7i 3. 5±i Please tell me how to get them. I have no clue on how to solve them.

    asked by Glenn on August 27, 2014
  7. trigonometry

    Write the quadratic function whose zeros are: 1. 2+square root of 5, 2-square root of 5 2. 3+7i,3-7i 3. 5±i Please tell me how to get them. I have no clue on how to solve them.

    asked by james on August 27, 2014
  8. Algebra

    I need help with a few questions, please explain. 1. Write a polynomial function in standard form with zeros -1, -1, 6. 2. Find the roots of the equation x^3 – 3x^2 + x + 5 3. Describe the number and type of roots for the

    asked by |-/ on January 31, 2018
  9. Pre-Calc

    A polynomial function f(x) with real coefficients has the given degree, zeros, and solution point. Degree: 3 Zeros: -2,2+2√2i Solution Point: f(−1) = −68 (a) Write the function in completely factored form. (b) Write the

    asked by Ben Dover III on March 2, 2018
  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

    asked by Pat on October 17, 2015

More Similar Questions