How would I solve for x in the equation x^3-9x^2-4=0?

Question

Sorry I keep asking so many questions, there is no summer tutor available for summer calc classes here.

Answer 1

There is only one real root and it is positive. Here's how I know.
x^3 - 9x^2 - 4 changes sign 1 time. This means there will be one positive root.
Replace x with -x.
(-x)^3 - 9(-x)^2 - 4
= -x^3 - 9x^2 - 4
This does not change signs. There are no negative roots.
The possible rational roots are the positive factors or 4.
1, 2 and 4 are the only possible rational roots. If none of these work, then that means the root is irrational, so you will have to approximate it.
I used my calculator to find it.
x = 9.048851

Answer 2

substitute x = y+3 to get the cubic equation into reduced form.
y^3 - 27y - 58 = 0
Then use Cardano's formula.
The real root is exactly
x = (29 + 4√7)^⅓ + (29 - 4√7)^⅓ + 3 = 9.048850906....

The imaginary roots are:
x = -(u + v - 6)/2 ± √3(u - v)i/2

where u = (29 + 4√7)^⅓ and v = (29 - 4√7)^⅓

or x = -.02442548 ± 0.66441588i

Answer 3

As you said above, there is no summer tutor for your classes.

I think that students should find tutors and take classes when they are approriate for them to take. Tutoring is expensive and if that is what you need, then you should pay for that rather than ask for random help from Answers.

I apologize for being negative. But, I don't think that "Answers" is to serve as your tutor and/or do your homework.

Answer 4

I would use a graphing calculator. Because its third order there are at max 3 roots (one per order).

First answer:
Graph and look for where it crosses the x-axis. Use a built-in root finding method to get the value of that zero. Wash, rinse, repeat.
Its fast for on tests, and accurate.

Theres longer algebraic methods if you like too.
Theres a couple of tricks, but they require good guesses for roots.

Answer 5

Calc solver online

http://www.calc101.com/webMathematica/sketch.jsp#topdoit

Here is how to find roots using a ti85
http://archives.math.utk.edu/visual.calculus/1/vertical.3/index.html

Answer 6

Most people just get out their graphing calculators, graph the line, and have the calculator figure out the roots for you. There is often more than one answer.

Answer 7

www.quickmath.com will answer it for you, sorry i couldn't be of much more help.