SOLUTION: What is a quartic function with only the two real zeros given? x = -4 and x = -1

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Question 687566: What is a quartic function with only the two real zeros given?
x = -4 and x = -1
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
There are three possibities with the coefficient of x4 = 1

1. x=-4 has multiplicity 1 and x=-1 has multiplicity 3

f(x) = (x+4)(x+1)³
f(x) = (x+4)(x+1)(x+1)(x+1) 
       Multiply that out and get:
f(x) = x4 + 7x3 + 15x2 + 13x + 4 


2. x=-4 has multiplicity 2 and x=-1 has multiplicity 2

f(x) = (x+4)²(x+1)²
f(x) = (x+4)(x+4)(x+1)(x+1) 
       Multiply that out and get:
f(x) = x4 + 10x3 + 33x2 + 40x + 16 


3. x=-4 has multiplicity 3 and x=-1 has multiplicity 1

f(x) = (x+4)³(x+1)
f(x) = (x+4)(x+4)(x+4)(x+1) 
       Multiply that out and get:
f(x) = x4 + 13x3 + 60x2 + 112x + 64 

Edwin
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