# using a polynomial equation

• Mar 25th 2008, 09:49 AM
using a polynomial equation
Any help will be greatly appreciated

An envelope is 4cm longer then it is wide. The area is 96 sq. cm Find the length and width. Use a polynomial equation.
• Mar 25th 2008, 09:57 AM
Peritus
$
\begin{gathered}
S_{envelope} = w(w + 4) = 96 \hfill \\
w^2 + 4w - 96 = 0 \hfill \\
\end{gathered}$

solve the quadratic equation to obtain the solution
• Mar 25th 2008, 10:32 AM
am i doing this correctly?
w-12=0
+12 +12
w=12

w+8=0
-8 -8
w=-8
• Mar 25th 2008, 10:50 AM
mathceleb
Quote:

am i doing this correctly?
w-12=0
+12 +12
w=12

w+8=0
-8 -8
w=-8

Plug your numbers in back into the original equation for Area and see. Hint: Remember that width, length, cannot be negative.
• Mar 25th 2008, 11:27 AM
would it be
12(12+4)=96
• Mar 25th 2008, 11:40 AM
iknowone
12*(12+4)= 12*16 =192 so that's cant be right.

the factoring of your polynomial should be (x-8)(x+12) which gives you x-8 = 0 or x+12 = 0, meaning x=8 or x=-12. Since x is a length and cant be negative the answer must be x=8.

Does it work?

8*(4+8) = 8*12 = 96!
• Mar 25th 2008, 11:48 AM
so what i was doing before
w-12=0
+12 +12
w=12

w+8=0
-8 -8
w=-8
was going in the total wronge direction?
• Mar 25th 2008, 01:08 PM
iknowone
No, it is just that your signs were backwards.

(w-8)(w+12) = w^2 + 4w - 96

where as

(w+8)(w-12) = w^2 - 4w - 96

Notice that the first quadratic equation is the one you are working with. The second equation above is similar to the first but the middle w-term is negative when it should be positive.