Question

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?

Answer 1

Will become fan and add medal

Answer 2

lol

Answer 3

Hi @Nnesha, do you think you can help?

Answer 4

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

Answer 5

looks like p/q method would work

Answer 6

i think i have to find the factors of -6 and put them over the factors of 1 right?

Answer 7

\[\rm \frac{ p }{ q }=\frac{ \pm factors~ of~constant }{ \pm factors~of ~leading~coefficient }\]

Answer 8

Yes...

Answer 9

yep that's correct and then test each possible solution by either using synthetic division or replacing x for its value

Answer 10

so i would end up with \[\frac{ 3 }{ 1 }, \frac{ 2 }{ 1 }, \frac{ 6 }{ 1 }, \frac{ 1 }{ 1 }\]

Answer 11

it should be plus/minus

Answer 12

of course sorry i forgot

Answer 13

then i would plug either +/-3, +/-2, +/- 6, +/-1 into my function and observe which number results in f(x) = 0. Right?

Answer 14

yep
and remember if there are duplicates numbers after dividing p/q u should eliminate it

Answer 15

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.

Answer 16

so would i synthetically divide x-1 by x^3 + 4x^2 + x - 6
(I'm terrible at math so i apologize)

Answer 17

Yes,

Answer 18

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

Answer 19

Ill try both your methods although the second seems more time consuming so ill try synthetic division first

Answer 20

true that if you are familiar with the synthetic division method then ofc do that first.

Answer 21

ok so i got x-1, x+3, and x + 2

Answer 22

i synthetically divided the inverse of each number and they all gave me a reminder of 0

Answer 23

looks good to me.

Answer 24

Thank you so much for the help, you both were wonderful help! :) XD

Answer 25

np. good work btw
keep it up!

Answer 26

Ill go ahead and close the question now.