polynomial degrees / multiplicities of zeroes / etc

M

marshall1432

Banned
Joined
Jan 10, 2007
Messages
80
1. Determine whether or not the following function is a polynomial. If so, give its degree; if not, explain why. f sqrt4

yes.

2. Determine the degree of the polynomial function
f (x) = 4

3rd degree

3. For the polynomial function below, list each real zero and its multiplicity.
f (x) = 4(x2 + 1)3(2x + 3)

(1,3) multiplicity=1

4. Write the equation for a polynomial function which has no real zeros.

3(x^2-2x^3+1)

5. Use your graphing calculator to determine the number of turning points on the graph of the polynomial function
f (x) = 3x3 - 56x2 - 12

2
 
1)
f[x]= sqrt 4
f[x]=+/-2
a polynomial of order 0

you plot this on a xy graph as two horizontal lines, one at y=+2 and one at y=-2



2)
f[x]=4
polynomial of order 0
a straight horizontal line at y=4

3)
f[x]= 4 [x^2+1]^3 [2x+3]
f[x]= 4[2] [x+1]^3[x-1]^3[x+1/2]
real zeros at:
x=-1,1,3/2

x=-1,1 have 3rd multiplicity zeros

4)
does f[x] have real roots?
f[x]= -2x^3+x^2-1

yes a real root at x=1
f[1]=-2+1-1
f[1]=0

function with no real roots
f[x]=[x+j[x-j] j=sqrt[-1]
f[x]=x^2+1 a second order polynomial with 2 imaginary roots

Arthur
 
im sorry, on #1 it should have been sqrt of x not 4. and also, can you explain 4 and 5 to me? thanks
 
4)

I must have goofed. I thought the last term was +1
f[x]= -2x^3+x^2-1
Does this function have real roots, or zeros?
this is the same as asking[ for what real values of x does the equation equal 0

f[x]= -2x^3 +x^2-1

f[0]=-1
f[1]= -2
f[2]= -15 as x increases f[x] keeps decreasing and never crosses the x axis

f[-1]=2+1-1
f[-1]=2
The function goes to 0 some where between x=-1 and x=0
thus a real zero

Arthur
 
1)
sqrtx=4 square both sides
x=16 a horizontal line at y=16

I would define this as a polynomial of order 0, zero x terms. All value of x have the same y value 16
Arthur
 
I can't do #5 because I do not have a calculator that graphs.

I will tell you that the curve reaches a maximum or a minimum where the derivative =0.
f[x]=3x^3-56x^2+2 take the derivative
df/dx = 9x^2-112 x set the derivative equal to zero
0=9x^2-112x factor
0=x[9x-112]
x=0 or x=112/9

f[x] changes direction at x=0 and at x=112/9

Arthur
 
marshall1432 said:
i didnt get any of 4 or 5, i dont even know what you are talking about.
Click to expand...
So you're not familiar yet with polynomials, zeroes, graphing, or any of the other topics which are foundational to these questions...? You've never worked with quadratics that didn't have two real solutions...? You've never used a graphing calculator...?

We understand (from previous threads and other correspondence) that you are taking an online class and that you feel that you are receiving little or no instruction or other assistance from your school.

But you need to understand that we simply cannot replace the missing instructional hours. To cover the many concepts of which you have exhibited little understanding, let alone mastery, it is strongly recommended that you hire a tutor and spend a few hours a day with him, obtaining the necessary lessons and help.

My best wishes to you.

Eliz.
 
You must log in or register to reply here.
Top