SOLUTION: What would be an equation with the solutions 5+2i,5-2i

Question 14578: What would be an equation with the solutions 5+2i,5-2i
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
What would be an equation with the solutions 5+2i,5-2i?
There are 2 solutions given here.As per theory of equations ,if we have to have 2 solutions for an unknown variable called x ,then the equation has to be a polynomial, say f(x)=0 , of degree 2 in x.Further ,the fact that it has one or more solutions implies ,that on substitution of that value for x in f(x),it has to equal zero,that is if say x=a is a solution of f(x)=0 ,then f(a) should equal to zero.That is as per Remainder theorem (x-a)is a factor of f(x).Hence we have
f(x) has 2 factors namely x-(5+2i) and x-(5-2i) corresponding to the 2 solutions given.Hence
is the basic equation which gives us the given solutions

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