if x=.28 determine the three real solutions (zeros) of F(X)=x^5-7x^4+10x^3+14x^2-21x

- anonymous

if x=.28 determine the three real solutions (zeros) of F(X)=x^5-7x^4+10x^3+14x^2-21x

- jamiebookeater

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- anonymous

What does it mean by if x=0.28?

- anonymous

it's a function and .28 has to be plugged in where there is an X

- anonymous

Okay x^5-7x^4+10x^3+14x^2-21x=0
x(x^4-7x^3+10x^2+14x-21)=0
So one solution is x=0.
If we divide through by x we are left with
x^4-7x^3+10x^2+14x-21=0
which has two complex solutions and two real ones.

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## More answers

- anonymous

i did not get the last part???

- anonymous

I just took the x to the other side so I would be left with
x^4-7x^3+10x^2+14x-21=0
I check wolfram and the are two real solutions and two complex one.
http://www.wolframalpha.com/input/?i=x^5-7x^4%2B10x^3%2B14x^2-21x
These other solutions we can estimate but not find exact answers.

- anonymous

What grade/ level are you in?

- anonymous

i am in high school senior year

- anonymous

Okay good, one way we can estimate is by graphing it on your graphics calculator and have it estimate the other two solutions.
Another way is to write it up in a program and use Newton's Method or another root finding tool.

- anonymous

yeah i have a graphing calc so how would i do it? if u can help me!!! please

- anonymous

Okay first off we need to graph y=x^5-7x^4+10x^3+14x^2-21x, are you able to do this?
What model/brand is your graphics calculator?

- anonymous

ok hold on

- anonymous

TI-84 texas

- anonymous

okay i graphed it

- anonymous

Good, that's the calculator I had in high school too. Makes this easier.

- anonymous

ok

- anonymous

so what do i do now?

- anonymous

Now press 2nd Trace

- anonymous

ok

- anonymous

I don't have the calculator anymore, but there should be some option called zeros or roots. Choose that option

- anonymous

ok

- anonymous

it says lef bound? right bound?

- anonymous

good, now for the left bound you want to choose the closest point you can get before the graph crosses the x axis
for the right bound you want to get it as close to x axis after you've crossed it.

- anonymous

Remeber you have to do this step for each point the graph crosses the x-axis.
So for your function you need to do this 3 times to get all the real roots.

- anonymous

ok

- anonymous

What answers are you getting?

- anonymous

-1.36823 and 1.18796

- anonymous

Good work, that's correct. :D

- anonymous

yay thanks to u

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