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Math Help - can somebody help me with these polynomials

  1. #1
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    can somebody help me with these polynomials

    A)The polynomial x3 is divided by x +3. Calculate the remainder.
    B)The polynomial p(x)is given by p(x)=ax3 +16x2+cx – 120, where a and c are constants. The three zeros of p(x)are –2, 3 and α. Find the value of α.
    c)The function ƒ()x =tanx −loge xhas a zero near x =4.Use one application of Newton’s method to obtain another approximation to this zero. Give your answer correct to two decimal places.
    d)The polynomial P(x)=x2+ax +b has a zero at x =2. When P(x)is divided by x +1, the remainder is 18.Find the values of a and b.
    e)The cubic polynomial P(x) =x3 +rx2 +sx +t
    , where r, s and t are real numbers, has three real zeros, 1, αand –α.
    (i) Find the value of r.
    (ii) Find the value of s +t.
    P(x) =x3 +rx2 +sx +t.

    p.s im sorry if this is in the wrong part of the forum this is my first post ever.
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  2. #2
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    Quote Originally Posted by andy69 View Post
    A)The polynomial x3 is divided by x +3. Calculate the remainder.
    B)The polynomial p(x)is given by p(x)=ax3 +16x2+cx – 120, where a and c are constants. The three zeros of p(x)are –2, 3 and α. Find the value of α.
    c)The function ƒ()x =tanx −loge xhas a zero near x =4.Use one application of Newton’s method to obtain another approximation to this zero. Give your answer correct to two decimal places.
    d)The polynomial P(x)=x2+ax +b has a zero at x =2. When P(x)is divided by x +1, the remainder is 18.Find the values of a and b.
    e)The cubic polynomial P(x) =x3 +rx2 +sx +t
    , where r, s and t are real numbers, has three real zeros, 1, αand –α.
    (i) Find the value of r.
    (ii) Find the value of s +t.
    P(x) =x3 +rx2 +sx +t.

    p.s im sorry if this is in the wrong part of the forum this is my first post ever.
    A) Use the remainder theorem.

    If P(x) is divided by x - a, the remainder is the same as P(a). What do you think "a" has to be in this case?
    Last edited by Prove It; May 19th 2010 at 02:06 AM.
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    Quote Originally Posted by Prove It View Post
    A) Use the remainder theorem.

    If P(x) is divided by x - \alpha, the remainder is the same as P(\alpha). What do you think \alpha is in this case?
    does the post have to be over 10 to view the links
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    Quote Originally Posted by andy69 View Post
    does the post have to be over 10 to view the links
    I didn't post any links. I've just used the LaTeX math type, it should just show up...
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    Quote Originally Posted by Prove It View Post
    I didn't post any links. I've just used the LaTeX math type, it should just show up...
    this is what it says about your latex math type.To view links or images in signatures your post count must be 10 or greater. You currently have 2 posts.
    can you post it up in a different way please because i need to practice these urgently.
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    Edited
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    Quote Originally Posted by Prove It View Post
    Edited
    sorry you just posted the same thing and it says the same thing of the post i previously posted if you dont get what i mean then dont worry about it
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    I edited my post so that it can be read by new posters. I have also basically given you the answer.

    Again - the remainder theorem states that if P(x) is divided by "x - a", then the remainder is the same as P(a).

    If you're dividing by "x + 3", what do you think "a" has to be? Work out P(a).
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    Quote Originally Posted by Prove It View Post
    I edited my post so that it can be read by new posters. I have also basically given you the answer.

    Again - the remainder theorem states that if P(x) is divided by "x - a", then the remainder is the same as P(a).

    If you're dividing by "x + 3", what do you think "a" has to be? Work out P(a).
    ok then does this method work for all my questions.
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  10. #10
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    Quote Originally Posted by andy69 View Post
    ok then does this method work for all my questions.
    Why not first make sure you understand the first question, then have a think about which ones you think the remainder theorem would apply to..?
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