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  1. #1
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    help solve 2

    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.

    with working out please
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  2. #2
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    Quote Originally Posted by andy69 View Post
    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.

    with working out please
    You have P(x) = x^2 + ax + b.


    By the Remainder and Factor Theorems:

    If there is a root at x = 2, then P(2) = 0.

    If, when you divide by x + 1 you get a remainder of 18, then P(-1) = 18.


    So you have:

    2^2 + 2a + b = 0

    (-1)^2 - a + b = 18.


    Simplify and solve these equations simultaneously for a and b.
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  3. #3
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    Quote Originally Posted by Prove It View Post
    You have P(x) = x^2 + ax + b.


    By the Remainder and Factor Theorems:

    If there is a root at x = 2, then P(2) = 0.

    If, when you divide by x + 1 you get a remainder of 18, then P(-1) = 18.


    So you have:

    2^2 + 2a + b = 0

    (-1)^2 - a + b = 18.


    Simplify and solve these equations simultaneously for a and b.
    so i get 4+2a+b=0(1) and 1-a+b=18(2)
    then i make 1-a+b=18(times by 2) which is 2-2a+2b=36(3)
    by elimination method
    (3)+(1)
    6+3b=36
    3b=30
    b=10
    sub b=10 into (1)
    4+2a+10=0
    2a=-14
    a=-7

    is this right?
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  4. #4
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    Quote Originally Posted by andy69 View Post
    so i get 4+2a+b=0(1) and 1-a+b=18(2)
    then i make 1-a+b=18(times by 2) which is 2-2a+2b=36(3)
    by elimination method
    (3)+(1)
    6+3b=36
    3b=30
    b=10
    sub b=10 into (1)
    4+2a+10=0
    2a=-14
    a=-7

    is this right?
    Yes, well done.
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  5. #5
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    Quote Originally Posted by Prove It View Post
    Yes, well done.
    thanks for the help
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