Expert: Sherman D. - 9/25/2004

Question
1) if 2 is a zero of p(x)= 3x^2 + kx -8, find the value of k.
2) a rectangular enclosure is to be made using a barn as one side and 80 m of fencing to form the other 3 sides. what is the maximum area of such an enclosure?

Answer
1.)
p(x) = 3x^2 + kx - 8

Using synthetic division, you get a remainder of 2k + 12 - 8, which becomes 2k + 4, and since 2 is a zero, division can't have a remainder, so you get,

2k + 4 = 0
2(k + 2) = 0
k + 2 = 0
k = -2

3x^2 - 2x - 8

For proof, if you use the quadratic formula, you get

x = 2 or -4/3

which becomes

(3x + 4)(x - 2)

which becomes

3x^2 - 2x - 8

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2.)

A = LW
P = 2W + L

Since there are only 3 sides, then we have only 2 sides equal and one remaining.

80 = 2W + L
-L = 2W - 80
L = -2W + 80

A = LW

A = (-2W + 80)(W)
A = -2W^2 + 80W

Using W = -b/(2a) to get maximum possibility

W = -80/(2(-2))
W = -80/(-4)
W = 20

Now just plug that in for W into A = -2W^2 + 80W

A = -2(20)^2 + 80(20)
A = -2(400) + 1600
A = -800 + 1600
A = 800m^2

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Proof

L = -2W + 80
L = -2(20) + 80
L = -40 + 80
L = 40

W = 20

A = LW
A = 40 * 20
A = 800m^2

that was what i got. If you like you can check with other experts to see what they get.