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# C4 quick question

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1. C4 quick question
Solve for P

P^3=21p+20

What methods could you use?
2. Re: C4 quick question
p^3-21p-20=0

Look at the coeffficients. 1, -21, -20.

With p=-1 you have -1+21-20=0.

Next you could divide by p+1.
3. Re: C4 quick question
(Original post by BabyMaths)
p^3-21p-20=0

Look at the coeffficients. 1, -21, -20.

With p=-1 you have -1+21-20=0.

Next you could divide by p+1.
Or if it wasn't so obvious to find, the first root, you could use the Newton-Raphson method:

But then once the first root is found, divide through and solve the quadratic.
4. Re: C4 quick question
(Original post by Transcendence)
Or if it wasn't so obvious to find, the first root, you could use the Newton-Raphson method:

But then once the first root is found, divide through and solve the quadratic.
How do you know when you've found a root with the newton raphson method?
5. Re: C4 quick question
(Original post by Super Mario 64)
How do you know when you've found a root with the newton raphson method?
It doesn't find roots, it approximates them.
6. Re: C4 quick question
(Original post by james22)
It doesn't find roots, it approximates them.
When the answer on the calculator doesn't change, you've found one though tbh. It will approximate though, like he said.
7. Re: C4 quick question
(Original post by Super Mario 64)
How do you know when you've found a root with the newton raphson method?
Do it by inspection.

Newton-Raphson is in FP1, if you are doing edexcel, so it isn't required for C4.

You may like to read about rational root theorem if you struggle to find the obvious root.
8. Re: C4 quick question
(Original post by Transcendence)
When the answer on the calculator doesn't change, you've found one though tbh. It will approximate though, like he said.
It will take too long, its best done by inspection.
9. Re: C4 quick question
(Original post by raheem94)
It will take too long, its best done by inspection.
is inspection basically trial and error?
10. Re: C4 quick question
(Original post by Super Mario 64)
is inspection basically trial and error?
Yes. You can just try in some values and see which one is the factor.

Or if you have a fx-991es, it can automatically find the roots of a cubic.
11. Re: C4 quick question
Are the solutions up?

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Last updated: June 22, 2012
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