SOLUTION: If c is a nonzero constant such that x^2+cx+9c is equal to the square of a binomial, then what is c?

SOLUTION: If c is a nonzero constant such that x^2+cx+9c is equal to the square of a binomial, then what is c?

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Question 1075591: If c is a nonzero constant such that x^2+cx+9c is equal to the square of a binomial, then what is c?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The discrimant has to equal 0 for the roots to be the same
sqrt(b^2-4ac) becomes sqrt(c^2-4*9*c)=sqrt(c^2-36c)
That equals 0, so c^2-36c=0
c=0,36, and 0 isn't allowed
c=36
x^2+36x+324=0
This is (x+18)^2=0
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