Algebra problem using graphing calc

[5ymmetrica1]

Hey guys I was given an assignment as part of my intro to calculus course, but I am not sure what the question is actually asking me to find or solve

Homework Statement

use a graphics calculator to solve the following equation
2x^3 - 3x^2 - 11x + 6 = 0

am I looking for the zeros of the function or am I trying to solve for x? and how do I use a graphics calculator to solve this sort of equation? I can solve for x algebraically and I can use my calculator to find the x-intercepts but I don't know how to solve this problem with my calculator.

The Attempt at a Solution

I know the zero's of the functions are y= 0 when x= -2, 0.5 and 3 but I don't think this is what the question is asking for??

 

[mtayab1994]

Hey guys I was given an assignment as part of my intro to calculus course, but I am not sure what the question is actually asking me to find or solve

Homework Statement

use a graphics calculator to solve the following equation
2x^3 - 3x^2 - 11x + 6 = 0

am I looking for the zeros of the function or am I trying to solve for x? and how do I use a graphics calculator to solve this sort of equation? I can solve for x algebraically and I can use my calculator to find the x-intercepts but I don't know how to solve this problem with my calculator.

The Attempt at a Solution

I know the zero's of the functions are y= 0 when x= -2, 0.5 and 3 but I don't think this is what the question is asking for??

Well when you have a question like this you will have to factor it out and see where it equals zero ( which values of x make it equal to zero).

 

[5ymmetrica1]

ok so factorising its zeros I would get
(x-3)(2x-1)(x+2)

 

[5ymmetrica1]

or is it...

(x-3)(2x-1)(x+2)
---> (2x² - x - 6x + 3)(x + 2)
---> (2x³ - 7x - 3)(x + 2)
---> 2x³ + 4x² - 7x² - 14x + 3x + 6 = 0

THEN by collecting like terms I get the original equation...

---> 2x³ - 3x² - 11x + 6 = 0

so this equation has roots of x= -2, 0.5 and 3

 

[eumyang]

use a graphics calculator to solve the following equation
2x^3 - 3x^2 - 11x + 6 = 0

am I looking for the zeros of the function or am I trying to solve for x?

They mean the same thing.

and how do I use a graphics calculator to solve this sort of equation?

Assuming you have a TI-84, graph the function, change the window so that all x-intercepts are shown, and hit [2ND]->[TRACE]->Zero. Provide the left and right bounds, and you'll get the zero. Repeat the process as needed until you get all zeros. Check the calculator's manual.

 

[Mark44]

or is it...

(x-3)(2x-1)(x+2)
---> (2x² - x - 6x + 3)(x + 2)
---> (2x³ - 7x - 3)(x + 2)
---> 2x³ + 4x² - 7x² - 14x + 3x + 6 = 0

You started with an equation, so each subsequent step should involve an equation. The two sides of an equation are separated by =, not --->.

THEN by collecting like terms I get the original equation...

---> 2x³ - 3x² - 11x + 6 = 0

so this equation has roots of x= -2, 0.5 and 3

 

[SammyS]

...

Homework Statement

use a graphics calculator to solve the following equation
2x^3 - 3x^2 - 11x + 6 = 0

am I looking for the zeros of the function or am I trying to solve for x? and how do I use a graphics calculator to solve this sort of equation? I can solve for x algebraically and I can use my calculator to find the x-intercepts but I don't know how to solve this problem with my calculator.
...

This is essentially what eumyang said, but I'll say it again:

Solving the equation, $\displaystyle \ \ 2x^3 - 3x^2 - 11x + 6 = 0 \,, \$ for x,

is equivalent to finding the zeros of the function defined by $\displaystyle \ \ f(x) = 2x^3 - 3x^2 - 11x + 6 \ .$

 

[Ray Vickson]

This is essentially what eumyang said, but I'll say it again:

Solving the equation, $\displaystyle \ \ 2x^3 - 3x^2 - 11x + 6 = 0 \,, \$ for x,

is equivalent to finding the zeros of the function defined by $\displaystyle \ \ f(x) = 2x^3 - 3x^2 - 11x + 6 \ .$

Which is the same as finding the *roots* of $2x^3 - 3x^2 - 11x + 6.$

 

[epenguin]

And all this, I like to reflect, all polynomial equation solving, a lot of algebra, what fraction would you say Ray Vickson or anyone, of algebra, of math, of useful math? - is down to the peculiar property of 0, the only number that remains itself when multiplied by every other number.

 

[5ymmetrica1]

thanks for the replies everyone, as expected it was as simple as using my TI to find the zeros as eumyang mentioned which I know how to do. It was the wording of the problem which confused me as I was not sure what I was "solving"

Usually problems of this kind that I have encountered previously are worded something along the lines of "find the zeros of the function y = ...... or f(x) = ........"

and mark44 I know that each side of the equation is separated by =, the ---> was simply an quick easy way of saying "goes to", it's bad mathematical notation I know so in future Ill be sure to use the correct symbols when posting on the forum :)

thanks again everyone
-5ym

 

[HallsofIvy]

Which is the same as finding the *roots* of $2x^3 - 3x^2 - 11x + 6.$

No, technically, it is not. Functions, including polynomials, have "zeros" but only equations have "roots".

 

[Ray Vickson]

No, technically, it is not. Functions, including polynomials, have "zeros" but only equations have "roots".

Not all sources agree. See
http://www.sosmath.com/algebra/factor/fac02/fac02.html or
http://tutorial.math.lamar.edu/Classes/Alg/ZeroesOfPolynomials.aspx or
http://mathworld.wolfram.com/PolynomialRoots.html .

Whether or not we like the terminology, the OP may well see it in future; if so, he/she will now know what is meant.