Question

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

Answer 1

What does it mean by if x=0.28?

Answer 2

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

Answer 3

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.

Answer 4

i did not get the last part???

Answer 5

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.

Answer 6

What grade/ level are you in?

Answer 7

i am in high school senior year

Answer 8

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.

Answer 9

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

Answer 10

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?

Answer 11

ok hold on

Answer 12

TI-84 texas

Answer 13

okay i graphed it

Answer 14

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

Answer 15

ok

Answer 16

so what do i do now?

Answer 17

Now press 2nd Trace

Answer 18

ok

Answer 19

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

Answer 20

ok

Answer 21

it says lef bound? right bound?

Answer 22

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.

Answer 23

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.

Answer 24

ok

Answer 25

What answers are you getting?

Answer 26

-1.36823 and 1.18796

Answer 27

Good work, that's correct. :D

Answer 28

yay thanks to u