SOLUTION: find a polynomial fuction of the smallest possible degree that will satisfy the following conditions: f(1)=f(3)=f(6)=0 ; f(4)=-12 ty

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Question 7705: find a polynomial fuction of the smallest possible degree that will satisfy the following conditions:
f(1)=f(3)=f(6)=0 ; f(4)=-12
ty
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
you have 3 roots, at x=1, x=3 and x=6, so we are taking about a cubic, where (x-1)(x-3)(x-6) = 0. The following graph shows just 3 of the possible curves:

graph%28200%2C+200%2C+-1%2C+7%2C+-10%2C+25%2C+%28x-1%29%28x-3%29%28x-6%29%2C+5%28x-1%29%28x-3%29%28x-6%29%2C+0.4%28x-1%29%28x-3%29%28x-6%29%29

the issue is now to find that ONE curve that passes through (4, -12). All the possible curves are just "multiples" of y = (x-1)(x-3)(x-6).

So, we have y = a(x-1)(x-3)(x-6), where a is a constant, so now put in the x and y values.

-12 = a(4-1)(4-3)(4-6)
-12 = a(3)(1)(-2)
-12 = -6a
--> a = 2

so, our required curve is y = 2(x-1)(x-3)(x-6)

jon.