+9481 1) When y = 0 , x = 1, 3, or -4
A polynomial in that form with zeros at 1, 3, and -4 is
y = a(x - 1)(x - 3)(x + 4)
To find a , plug in -1 for x and 2 for y .
2 = a(-1 - 1)(-1 - 3)(-1 + 4)
2 = a(-2)(-4)(3)
2 = 24a
a = 1/12
So the polynomial is y = (1/12)(x - 1)(x - 3)(x + 4) And here's a graph to check it.
2) We want to know what p is when supply = demand . That is, when
6 + 0.001p3 = 80 - 0.02p2
Let's solve this using a graph. The p value that makes the equations have the same y value is
p ≈ 36.27
Look at the graph or plug this value for p into either function to find out how many hair dryers are supplied and demanded at this price.
D( 36.27 ) = 80 - 0.02( 36.27 )2 ≈ 53
