Question

Explain how to find the zeros of the function
f(x) = 2x3 – 9x + 3. Help, please:)

Answer 1

f(x)=2x^3-9x+3

Answer 2

Let x = (a+b). Then x^3 = (a+b)^3 = a^3 + 3 a b (a + b) + b^3 = a^3 + 3 a b x+ b^3, or

x^3 - 3 a b x - (a^3+b^3) = 0

Solve 3 a b = 9, and - (a^3+b^3) = 3

Then the answer is x = a + b

x1= 3^(2/3)/(1/2 (-1 + i sqrt(11)))^(1/3) + (3/2 (-1 + i sqrt(11)))^(1/3)

x2 = -(((3/2)^(2/3) (1 +i sqrt(3)))/(-1 +i sqrt(11)^(1/3)) -
1/2 (1 -i sqrt(3)) (3/2 (-1 +i sqrt(11)))^(1/3)

x3 = -(((3/2)^(2/3) (1 -i sqrt(3)))/(-1 +i sqrt(11))^(1/3)) -
1/2 (1 +i sqrt(3)) (3/2 (-1 + i sqrt(11)))^(1/3)

Answer 3

Does that help, a little? :3

Answer 4

It's a bit confusing but I'll find a way. Thanks you:)

Answer 5

If anyone else has different methods of solving something like this please share:)

Answer 6

@jackoo two questions:

1. Are you sure you copied the problem correctly (I tried a few variations of it, none have "nice" roots.

2. What sort of answer are you looking for? Deriving the cubic equation? Numerical approximation? Graphing?

Answer 7

write it out in factored form, then mulitply out. say you want the zeros to be -2, 3 and 1/2
the write out
(x+2)(x−3)(2x−1)

Answer 8

that obviously has zeros at -2, 3 and 1/2. multiply out to put it in standard form. i get
2x^3−3x^2−11x+6
but you can make up your own

Answer 9

just pick the zeros, write in factored form, and then multiply out. much easier than last problem, yes.

Answer 10

Yes, I wrote it incorrectly but I corrected the equation.
f(x)=2x^3-9x+3

Answer 11

1) write in factored form (don't show anyone)
2) multiply it out
3) factor again, you will get what you started with
4) now you know the zeros

Answer 12

Thank you @dumbsearch2 and @mathteacher1729 do you have a different method?

Answer 13

(BTW if it helps, I would greatly appreciate if you could mark my answer as correct. ^_^)

Answer 14

Will do:)

Answer 15

:) Oh, and you'll find all the answers you need here: https://www.google.com/search?q=f(x)+%3D+2x3+%E2%80%93+9x+%2B+3&oq=f(x)+%3D+2x3+%E2%80%93+9x+%2B+3&aqs=chrome.0.57j62l3j60.305&sourceid=chrome&ie=UTF-8#hl=en&safe=off&tbo=d&sclient=psy-ab&q=f(x)+%3D+2x3+%E2%80%93+9x+%2B+3+site:openstudy.com&oq=f(x)+%3D+2x3+%E2%80%93+9x+%2B+3+site:openstudy.com&gs_l=serp.3...4270.6327.0.6503.19.19.0.0.0.0.211.2828.0j16j2.18.0.les%3B..0.0...1c.1.3.psy-ab.a95BNdOitko&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.&bvm=bv.42553238,d.aWc&fp=9d6268e7630cf0ae&biw=1280&bih=624 You'd be suprised about how a simple Google search helps you find everything. :)

Answer 16

A lot of questions here have been asked previously.