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# Core 1 question (Stationary points etc) Watch

1. Qi) Find the coordinates of the stationary points on the graph of

I've done that and the stationary points are:

Now it says:

ii) Hence write down the set of values of the constant for which the equation has three distinct real roots.

Hmm, I'm not sure.
2. Sketch/visualise the graph, you want values of k for which intesects 3 times. You can get the answer easily from your answer to the first part
3. (Original post by dnumberwang)
Sketch/visualise the graph, you want values of k for which intesects 3 times. You can get the answer easily from your answer to the first part
So do you use 0 and 2/27? I understand that I think but in the answers they use the inequalities; I can't understand how you use them to show 3 roots...
4. (Original post by Dededex)
are you sure?
5. (Original post by Pheylan)
are you sure?
Hmm I was gonna ask - the answer in book give 4/27 but surely if x = -1/3 then:

Then add 1/9 (3/27) to -1/27 you get 2/27?
6. (Original post by Pheylan)
are you sure?
I just noticed that as well

(Original post by Dededex)
So do you use 0 and 2/27? I understand that I think but in the answers they use the inequalities; I can't understand how you use them to show 3 roots...
The equation will have 3 roots whenever
7. nvm spotted it.
8. (Original post by Dededex)
Hmm I was gonna ask - the answer in book give 4/27 but surely if x = -1/3 then:

Then add 1/9 (3/27) to -1/27 you get 2/27?
so perhaps x isn't -1/3
9. Differentiate it again. You will see where you have gone wrong. Particularly the x^2
10. (Original post by Pheylan)
so perhaps x isn't -1/3
Hmm perhaps you are right - infact, perhaps I have indeed differentiated wrong!

..

Wait, yeah I have! Sorry
11. (Original post by dnumberwang)
I just noticed that as well

The equation will have 3 roots whenever
hmm well the answer is 0 < k < 4/27

But I can't understand what that has to do with "3 distinct real roots" or what it means - all I can see from that is where y is increasing.
12. (Original post by Dededex)
hmm well the answer is 0 < k < 4/27

But I can't understand what that has to do with "3 distinct real roots" or what it means - all I can see from that is where y is increasing.
3 distinct real roots means that there are 3 different solutions to the equation . So the lines and will intersect 3 times. has no variables (x's) so it'll be horizontal

Sketch the graph of and think about what horizontal lines will intersect it 3 times
13. (Original post by dnumberwang)
3 distinct real roots means that there are 3 different solutions to the equation . So the lines and will intersect 3 times. has no variables (x's) so it'll be horizontal

Sketch the graph of and think about what horizontal lines will intersect it 3 times
Sorry even after I sketch it I can't understand - how can it intersect three times? What is the line y = k? eergh stupid question - don't worry I'll ask my teacher tomorrow or something I'm wasting your time on here to be honest
14. (Original post by dnumberwang)
3 distinct real roots means that there are 3 different solutions to the equation . So the lines and will intersect 3 times. has no variables (x's) so it'll be horizontal

Sketch the graph of and think about what horizontal lines will intersect it 3 times
Oh wait I think I see it - so if k is less than 4/27? But then if k is also less than zero won't it intersect 3 times?
15. (Original post by Dededex)
Oh wait I think I see it - so if k is less than 4/27? But then if k is also less than zero won't it intersect 3 times?
So k must be between 4/27 and 0

16. (Original post by dnumberwang)
So k must be between 4/27 and 0

Aah yes I see it now! Finally thank you so much - I think it's also because I had to account for the fact that k is the y value not the x value which I'm used to.

Thanks mate

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