# Find the values of M and N

• Jul 17th 2012, 06:05 PM
waleedrabbani
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
• Jul 17th 2012, 06:56 PM
Soroban
Re: Find the values of M and N
Hello, waleedrabbani!

Quote:

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

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

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

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

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

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

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

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

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