anonymous
  • anonymous
Please help I don't understand this at all: Approximate the real number solution(s) to the polynomial function f(x) = x3 + 4x2 + x − 6?
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Will become fan and add medal
Nnesha
  • Nnesha
lol
anonymous
  • anonymous
Hi @Nnesha, do you think you can help?

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More answers

Pawanyadav
  • Pawanyadav
We don't have a perticular formula for checking solution of a cubic polynomial. So we need to check it... Start with smallest factor of 6 ...X=1 ,if you get f(1) =0 ,than 1 is its solution
Nnesha
  • Nnesha
looks like p/q method would work
anonymous
  • anonymous
i think i have to find the factors of -6 and put them over the factors of 1 right?
Nnesha
  • Nnesha
\[\rm \frac{ p }{ q }=\frac{ \pm factors~ of~constant }{ \pm factors~of ~leading~coefficient }\]
Pawanyadav
  • Pawanyadav
Yes...
Nnesha
  • Nnesha
yep that's correct and then test each possible solution by either using synthetic division or replacing x for its value
anonymous
  • anonymous
so i would end up with \[\frac{ 3 }{ 1 }, \frac{ 2 }{ 1 }, \frac{ 6 }{ 1 }, \frac{ 1 }{ 1 }\]
Nnesha
  • Nnesha
it should be plus/minus
anonymous
  • anonymous
of course sorry i forgot
anonymous
  • anonymous
then i would plug either +/-3, +/-2, +/- 6, +/-1 into my function and observe which number results in f(x) = 0. Right?
Nnesha
  • Nnesha
yep and remember if there are duplicates numbers after dividing p/q u should eliminate it
Pawanyadav
  • Pawanyadav
Here, f(1)=0 Means (x-1) is its factor. You can find remaining factor by dividing f(x) by (x-1). You will get a quadratic equation And you know how to solve them.
anonymous
  • anonymous
so would i synthetically divide x-1 by x^3 + 4x^2 + x - 6 (I'm terrible at math so i apologize)
Pawanyadav
  • Pawanyadav
Yes,
Nnesha
  • Nnesha
or you can find \[\rm f(\pm1),f(\pm2) f(\pm 3),f(\pm6)\] and see which one give you 0 as final answer that would be the real zero ~zeros (x-intercept) is a point where the graph intersect the x-axis when y=0 and in this question f(x) is same as y
anonymous
  • anonymous
Ill try both your methods although the second seems more time consuming so ill try synthetic division first
Nnesha
  • Nnesha
true that if you are familiar with the synthetic division method then ofc do that first.
anonymous
  • anonymous
ok so i got x-1, x+3, and x + 2
anonymous
  • anonymous
i synthetically divided the inverse of each number and they all gave me a reminder of 0
Nnesha
  • Nnesha
looks good to me.
anonymous
  • anonymous
Thank you so much for the help, you both were wonderful help! :) XD
Nnesha
  • Nnesha
np. good work btw keep it up!
anonymous
  • anonymous
Ill go ahead and close the question now.

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