Polynomial arrays intersection and area within intersection

Hello,

I don't understand what is meant by polynomial array. I am wondering if it is as simple as what I wrote.

For part 2, I know I need to do some sort of fzero, but I'm not really sure. like fzero(f1,f2) or something along those lines.

Answer 1

[Roger Stafford]

@Rick. What Ahmet has given you does in fact help. Your mistake lies in assuming powers for matlab's 'intersect' function that it doesn't have. If you read its documentation you will see what I mean. What you need at this point is 'roots', not 'intersect'. Does that get you going again?

[Rick]

Well, roots will find me the roots for the polynomial, however, I am trying to find where these two polynomials will intersect. I don't understand how to find where they will intersect. I did plot(x,polyval(f1,x)) and plot(x,polyval(f2,x)) and saw the two polynomials. I am convinced about polyval, I just don't know how to find the intersection using roots.

[Roger Stafford]

You're so close to getting there it hurts! Think "difference", "difference", "difference"!

[Rick]

roots(polyval(f1,x)-polyval(f2,x))?? That gives a large column array with imaginary numbers.

[Roger Stafford]

That's not the way to get the coefficients of the difference between the polynomials. You're just getting the difference between their values that way. Think what 'roots' requires as an input.

[Roger Stafford]

Rick, if you haven't solved your problem yet, ask yourself this question. What polynomial is it that has as its roots the three intersection points that are being sought, and what are its coefficients?

[Rick]

I am still confused what it's supposed to be, I didn't understand your hint.

[Roger Stafford]

Here is my final hint, Rick. What do you think would be the result of:

 roots(f2-f1)

where f1 and f2 are the arrays referred to in part G.1 of your image.jpg ?

[Rick]

apparently it gives you the intersection. I don't understand how it does that, I did that command and it gave the intersection.

Answer 2

[Ahmet Cecen]

 help polyval

And the rest is your homework. Good luck.

[Rick]

I don't see how that helps. I don't have values for x. One thing I would like to stress is that this is supposed to be done by hand, I wouldn't even have matlab with me since this was an exam problem.

is

f1 = [0 -0.5 -3.5 4];
f2 = [-0.1 0 1.3 5];

intersect(polyval(f2,x),polyval(f1,x))

ans =

   Empty matrix: 1-by-0

[Ahmet Cecen]

 x=-6:0.1:12; %maybe even 0.01