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Math Help - Polynomial Functions Gr 12- Thinking and Inquiry Question

  1. #1
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    Polynomial Functions Gr 12- Thinking and Inquiry Question

    I have two Questions:

    any sort of help would help even a hint of what methods to use much appreciated

    i just need help with 1 of the 2 questions which ever is easier
    The reason i put 2 questions up is because one is copied of the board not sure if i copied it right other one is given from my text with the solution.

    1.)

    f(x)= 3x^3+b^2+cx+2

    Zeros (x-2) (x+3)

    solve for b and c

    2.)

    f(x)= 3x^4 +14x^3+px^2+qx+24 has x intercepts -4 and 2
    determine the function

    Solution: f(x)= 3x^4+14x^3-11x^2-70x+24
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by s.a.n.t.a.n.a View Post
    I have two Questions:

    any sort of help would help even a hint of what methods to use much appreciated

    i just need help with 1 of the 2 questions which ever is easier
    The reason i put 2 questions up is because one is copied of the board not sure if i copied it right other one is given from my text with the solution.

    1.)

    f(x)= 3x^3+bx^2+cx+2

    Zeros (x-2) (x+3)

    solve for b and c
    Are you missing an x at the place where I inserted it?

    When y=0, the function crosses the x-axis; these are the zeros.

    So (x-2) is a zero, and so is (x+3). This implies that x-2=0\implies x=2 and x+3=0\implies x=-3

    So plugging these two x values into the function, we should see that

    3(2)^2+b(2)^2+c(2)+2=0\implies 4b+2c=-14\implies 2b+c=-7

    3(-3)^2+b(-3)^2+c(-3)+2=0\implies 9b-3c=-29

    Can you solve this system of equations?

    \left\{\begin{array}{rcrcr}2b&+&c&=&-7\\9b&-&3c&=&-29\end{array}\right.


    2.)

    f(x)= 3x^4 +14x^3+px^2+qx+24 has x intercepts -4 and 2
    determine the function

    Solution: f(x)= 3x^4+14x^3-11x^2-70x+24
    This one follows the same idea as the previous problem. Plug these two values into the function, noting that when x=-4 and 2, f(-4)=f(2)=0. Then solve the system of equations.

    Can you take it from here?

    --Chris
    Last edited by Chris L T521; October 2nd 2008 at 08:20 AM.
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  3. #3
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    Ya i see what you did there but im still not sure how to solve for b c
    and i am not sure were you got the negitive 1 from
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