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URGENT - OCR FP1 Roots of Polynomials Watch

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    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.
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    it is quicker to learn them than faff around in the exam...
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    (Original post by the bear)
    it is quicker to learn them than faff around in the exam...
    Ok thanks.
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    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.
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    Please can someone help with the above.
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    (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 \alpha=\nu, \beta=\nu +d, \gamma=\nu + 2d

    At this point if you found one root, you may as well divide the polynomial through by x+1 and solve the remaining quadratic.

    Otherwise, \alpha+\beta+\gamma=-3=3\nu+3d

    And \alpha\beta+\beta\gamma+\gamma \alpha=7=3\nu^2+6d\nu+2d^2

    Now you have 2 equations in 2 unknowns and you can solve for \nu and d
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    (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 \alpha + \beta and \alpha\beta in terms of a,b then find what \frac{2}{\alpha}+\frac{2}{\beta} and \frac{2}{\alpha}\cdot \frac{2}{\beta} are in terms of \alpha+\beta, \alpha\beta hence in terms of a,b, then put them in a quadratic as required.
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    (Original post by RDKGames)
    They're in an arithmetic progression. So the roots are \alpha=\nu, \beta=\nu +d, \gamma=\nu + 2d

    At this point if you found one root, you may as well divide the polynomial through by x+1 and solve the remaining quadratic.

    Otherwise, \alpha+\beta+\gamma=-3=3\nu+3d

    And \alpha\beta+\beta\gamma+\gamma \alpha=7=3\nu^2+6d\nu+2d^2

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