Sketch/visualise the graph, you want values of k for which y=k intesects y=x3+x2 3 times. You can get the answer easily from your answer to the first part
Sketch/visualise the graph, you want values of k for which y=k intesects y=x3+x2 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...
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 x3+x2=k will have 3 roots whenever a<k<b
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 x3+x2=k. So the lines y=x3+x2 and y=k will intersect 3 times. y=k has no variables (x's) so it'll be horizontal
Sketch the graph of y=x3+x2 and think about what horizontal lines will intersect it 3 times
3 distinct real roots means that there are 3 different solutions to the equation x3+x2=k. So the lines y=x3+x2 and y=k will intersect 3 times. y=k has no variables (x's) so it'll be horizontal
Sketch the graph of y=x3+x2 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
3 distinct real roots means that there are 3 different solutions to the equation x3+x2=k. So the lines y=x3+x2 and y=k will intersect 3 times. y=k has no variables (x's) so it'll be horizontal
Sketch the graph of y=x3+x2 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?
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.