How can I find the value of n when given a polynomial equation?

[lioric]

Homework Statement

How do I find the value of n?

Homework Equations

I know that when it crosses x-axis y = 0
X³ - X² - 20 =0
But don't know how to solve it from here

The Attempt at a Solution

The marking scheme says 3.0 or 3.1
I couldn't get the answer even by substituting
I know I'm doing something stupid

 

[phinds]

Have you googled "how to solve a cubic equation" ?

 

[lioric]

The answer was there in the previous part
Thank you

 

[Mark44]

@lioric, what's the complete problem? In the image you posted, there is no "n".

 

[phinds]

@lioric, what's the complete problem? In the image you posted, there is no "n".

Look closer.

Squint like Clint

 

[Mark44]

I was already squinting, looking at that unclear and incomplete image. By "there is no n" I meant that the equation doesn't involve n.

 

[Ray Vickson]

Look closer.

View attachment 229330
Squint like Clint

When I looked at it the first time (on my phone) there was no n. When I looked at it later (on my laptop) there was, magically, an n.

 

[mathwonk]

If the answer is desired as a decimal, it seems that it is an infinite decimal, hence cannot be written down exactly. Thus the simplest way to approximate this decimal to a few places is to just plug in values. when x=2, we get 8 - 4 -20 = -16. when x=3 we get 27 - 9 -20 = -2. so we re getting closer. when x = 4 we get 64 - 16 - 20 = 28, so we are getting further away. hence the answer lies between 3 and 4, so next try 3.1 and then 3.2, etc..., and stop when you get a positive result. then if say 3.1 gives a negative result and 3.2 gives a positive result, you can choose the one that gives a result closer to zero, as a first decimal place approximation.

 

[sjb-2812]

If the answer is desired as a decimal, it seems that it is an infinite decimal, hence cannot be written down exactly.

Just be careful with your language. 0.33333333333333333333... (to infinity) is also an infinite decimal, but can be written exactly as ¹/₃.