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Math Help - Algebra woes

  1. #1
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    Algebra woes

    Hey guys,

    I'm new and find your abode in great despair..

    Im calling all maths guru...

    Any chance the maths gurus can help me answer these questions and show me the working out for each of them?

    They are like the last 4 questions I have(the hardest ones)

    1 a. P(x) is a polynomial.
    If P (a) =0
    State the factor theorem.

    b. Use the factor theorem to show that (x-2) is a factor of x3-x2-7x+2

    c. Substitute x=2, x=3, and x=1 and x= -1 into the polynomial P(x)= x3-4x2+x+6


    2 Express the quadratic x2-2x-3 in the form of (x+p)2+q where p and q are constants.

    a. Hence or otherwise find the coordinates of the vertex of the parabola y= x2-2x-3.

    b. Find the roots of x2-2x-3=0 and hence sketch the parabola y= x2-2x-3.


    3b. Express the following quadratics in the completed square form and solve them.

    i. X2-4x-3=0

    ii. X2+6x+4=0
    Last edited by mr fantastic; January 24th 2011 at 12:35 AM. Reason: Tidying things up.
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  2. #2
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    Quote Originally Posted by xirokx View Post
    1 a. P(x) is a polynomial.
    If P (a) =0
    State the factor theorem.
    This is easy, just state the rule.

    For P(x), if P(a) =0 then x-a is a factor

    Quote Originally Posted by xirokx View Post

    b. Use the factor theorem to show that (x-2) is a factor of x3-x2-7x+2
    Find P(2) if this equals zero you have shown it.

    Quote Originally Posted by xirokx View Post

    c. Substitute x=2, x=3, and x=1 and x= -1 into the polynomial P(x)= x3-4x2+x+6
    Find P(2),P(3),P(1) and P(-1)

    If any of these are zero then you have some factors.

    Quote Originally Posted by xirokx View Post

    2 Express the quadratic x2-2x-3 in the form of (x+p)2+q where p and q are constants.

    a. Hence or otherwise find the coordinates of the vertex of the parabola y= x2-2x-3.

    b. Find the roots of x2-2x-3=0 and hence sketch the parabola y= x2-2x-3.
    For this you need to complete the square, here's an example on how to do it.

    http://www.mathhelpforum.com/math-he...-question.html

    vertex will be (-q,p) in what you find.
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  3. #3
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    thanks,

    any ideas about this one:

    A solution to the equation X2 -5x+2=0 lies between 4
    and 5. Find this solution to two decimal place using
    “trial and improvement” method






    are you saying questions 2 and 3b are both "complete the square" type questions?

    please clarify..

    thanks
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  4. #4
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    Quote Originally Posted by xirokx View Post
    are you saying questions 2 and 3b are both "complete the square" type questions?

    please clarify..

    thanks
    Yep.

    Quote Originally Posted by xirokx View Post

    any ideas about this one:

    A solution to the equation X2 -5x+2=0 lies between 4
    and 5. Find this solution to two decimal place using
    “trial and improvement” method
    Find solution when x=4 and x=5, which is closer to zero?

    Then concentrate on checking solutions on the interval (4,5) closer to that point. Make sense?
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