Help solving for X-intercept please.

[Alpha6]

I was helping my younger cousin today with a problem and I was stuck!


The equation was X^{3 -}5x +2.

I figured set the equation equal to zero... but then I got stuck -_- (X³ -5X = -2)???

I saw the graph and figured '2' was one of the solution but I have no idea how to work this out. Help please.

 

[ksdhart]

The first thing I'd mention is that just because it looks like x=2 is a root on the graph doesn't necessarily mean it is. The root could just as easily be x=1.995 or x=2.005 and you'd not be able to tell by eyeballing it. However, in this case, a quick check by plugging in 2 for x reveals that it is, in fact, a root. That said, once you know one root, you're well on your way to finding the others. Because x=2 is a root of the polynomial, that means the polynomial must be evenly divisible by (x-2). What do you get when you do the division? You might find it helpful to review polynomial long division here.

 

[pka]

I was helping my younger cousin today with a problem and I was stuck!
The equation was X^{3 -}5x +2.

Looking at it, clearly 2 is a root so (x-2) is a factor.
\(\displaystyle (x-2)(x^2+2x-1)\) is the factored form.
Thus solve that.

 

[stapel]

I was helping my younger cousin today with a problem...

The equation was X^{3 -}5x +2.

This is not an equation, since it contains no "equals" sign; it is only an expression.

I will guess that there is a typo in the expression, and that "X" is really meant to be "x". Also, I will guess that you put the instructions in the subject line; namely, your cousin is supposed to be finding the x-intercepts of the related graph, y = x³ - 5x + 2. To learn how to solve polynomial equations of this sort, try here for a quick refresher of the terms and techniques.

In future, kindly please have your cousin post, so that we can work directly with the student. Thank you!