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Math Help - Find the values of M and N

  1. #1
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    Find the values of M and N

    I am lost in this question attached if some kind soul can show the algebra it would be highly appreciated
    Attached Thumbnails Attached Thumbnails Find the values of M and N-img_0690.jpg  
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  2. #2
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    Re: Find the values of M and N

    Hello, waleedrabbani!

    \text{Let: }\:\begin{array}{ccc}f(x) &=& mx^2+2x+5 \\ g(x) &=& 2x^2 + nx - 2 \end{array}

    \text{Define: }\:H(x) \;=\;f(x)\!\cdot\!G(x)

    \text{Two points that satisfy }H(x)\text{ are: }\,(1,\text{-}40)\text{ and }(\text{-}1,24).

    \text{Determine the values of }m\text{ and }n.

    H(x) \:=\:(mx^2+2x+5)(2x^2+nx-2)

    H(1) = \text{-}40
    . . (m + 2 + 5)(2 + n - 2) \:=\:\text{-}40 \quad\Rightarrow\quad mn + 7n \:=\:\text{-}40\;\;[1]

    H(-1) = 24
    . . (m - 2 + 5)(2-n-2) \:=\:24 \quad\Rightarrow\quad \text{-}mn - 3n \:=\:24\;\;[2]

    Add [1] and [2]: . 4n \,=\,\text{-}16 \quad\Rightarrow\quad \boxed{n \,=\,\text{-}4}

    Substitute into [2]: . 4m + 12 \:=\:24 \quad\Rightarrow\quad \boxed{m\,=\,3}
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