anonymous
  • anonymous
if x=.28 determine the three real solutions (zeros) of F(X)=x^5-7x^4+10x^3+14x^2-21x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
What does it mean by if x=0.28?
anonymous
  • anonymous
it's a function and .28 has to be plugged in where there is an X
anonymous
  • 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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anonymous
  • anonymous
i did not get the last part???
anonymous
  • 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
  • anonymous
What grade/ level are you in?
anonymous
  • anonymous
i am in high school senior year
anonymous
  • 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
  • anonymous
yeah i have a graphing calc so how would i do it? if u can help me!!! please
anonymous
  • 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
  • anonymous
ok hold on
anonymous
  • anonymous
TI-84 texas
anonymous
  • anonymous
okay i graphed it
anonymous
  • anonymous
Good, that's the calculator I had in high school too. Makes this easier.
anonymous
  • anonymous
ok
anonymous
  • anonymous
so what do i do now?
anonymous
  • anonymous
Now press 2nd Trace
anonymous
  • anonymous
ok
anonymous
  • anonymous
I don't have the calculator anymore, but there should be some option called zeros or roots. Choose that option
anonymous
  • anonymous
ok
anonymous
  • anonymous
it says lef bound? right bound?
anonymous
  • 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
  • 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
  • anonymous
ok
anonymous
  • anonymous
What answers are you getting?
anonymous
  • anonymous
-1.36823 and 1.18796
anonymous
  • anonymous
Good work, that's correct. :D
anonymous
  • anonymous
yay thanks to u

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