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URGENT - OCR FP1 Roots of Polynomials watch

1. I have attached an image of some identities for the cubic equations, but I am not sure if I am supposed to remember them or derive them in the exam. They are also not in the formula booklet.

I have tried tried to exam (α + β +gamma)^3 but it does not come out with following identity. I have been told that I need to know about this because they can ask to calculate α^3 + β^3 +gamma^3 in the exam, or something like that.

The attached identity is also in my book, so I suppose it is quite important to know.
Attached Images

2. it is quicker to learn them than faff around in the exam...
3. (Original post by the bear)
it is quicker to learn them than faff around in the exam...
Ok thanks.
4. Please can someone help me with question 2 and 3. the bear, RDKGames

For question 2, I used the remainder theorem and found that a one factor of f(x) is (x+1), therefore one root of the equation is x = -1

I also calculated the following values.

Sum of roots = -b/a = -3

c/a = 7

Product of roots = -d/a = -5

But unfortunately I am stuck and can't move forward.
Attached Images

5. Please can someone help with the above.
6. (Original post by phat-chewbacca)
Please can someone help me with question 2 and 3. the bear, RDKGames

For question 2, I used the remainder theorem and found that a one factor of f(x) is (x+1), therefore one root of the equation is x = -1

I also calculated the following values.

Sum of roots = -b/a = -3

c/a = 7

Product of roots = -d/a = -5

But unfortunately I am stuck and can't move forward.
They're in an arithmetic progression. So the roots are

At this point if you found one root, you may as well divide the polynomial through by and solve the remaining quadratic.

Otherwise,

And

Now you have 2 equations in 2 unknowns and you can solve for and
7. (Original post by phat-chewbacca)
Please can someone help me with question 2 and 3. the bear, RDKGames

For question 2, I used the remainder theorem and found that a one factor of f(x) is (x+1), therefore one root of the equation is x = -1

I also calculated the following values.

Sum of roots = -b/a = -3

c/a = 7

Product of roots = -d/a = -5

But unfortunately I am stuck and can't move forward.
For Q3, deduce your and in terms of then find what and are in terms of hence in terms of , then put them in a quadratic as required.
8. (Original post by RDKGames)
They're in an arithmetic progression. So the roots are

At this point if you found one root, you may as well divide the polynomial through by and solve the remaining quadratic.

Otherwise,

And

Now you have 2 equations in 2 unknowns and you can solve for and
Thanks a lot. That makes sense.

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Updated: July 22, 2017
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