SOLUTION: how do you determine an equation from the zeros for example -3/4, 2/5 -4+2(square root)3 -4-2(square root)3

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Question 29538: how do you determine an equation from the zeros
for example
-3/4, 2/5
-4+2(square root)3
-4-2(square root)3

Answer by AnlytcPhil(1808)   (Show Source): You can put this solution on YOUR website!
how do you determine an equation from the zeros 
for example 
-3/4, 2/5 
-4+2(square root)3
-4-2(square root)3 

To find a polynomial equation whose zeros are r1, r2, r3, r4, form the 
following equation, multiply it out and simplify it.

(x - r1)(x - r2)(x - r3)(x - r4) = 0
                            _          _
For r1=-3/4, r2=2/3, r3=-4+2Ö3, r4=-4-2Ö3)

Such an equation would be:
                             _             _ 
(x + 3/4)(x - 2/5)[x - (-4+2Ö3)][x - (-4-2Ö3)] = 0

Multiply that out -- a very big job -- then you'll get

x4 + (167/20)x3 + (13/2)x2 - x - 6/5 = 0

Clearing of fractions

20x4 + 167x3 + 130x2 - 20x - 24 = 0

Edwin
AnlytcPhil@aol.com


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