Monday
May 2, 2016

# Homework Help: Algebra II

Posted by K. on Tuesday, April 10, 2007 at 1:24pm.

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