SOLUTION: Given that the equation {{{kx^2+12x+k=0}}} where k is a positive constant and has equal roots. Find the value of k.

Question 664293: Given that the equation where k is a positive constant and has equal roots. Find the value of k.
Found 2 solutions by lynnlo, vleith:
Answer by lynnlo(4176) (Show Source): You can put this solution on YOUR website!
k=-12x/x^2+1
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
You are told to find k such that the given equation results in two equal roots.
That says the resulting answer will end up being in the form
So Let's expand that

Now lets match that up with the given problem
We see that , , and
We can see from this that and also that
Using the , we can see that either a=b or a=-b
Since a*b is positive (6), then a must be equal to b.
If a=b and ab =6, then a and b are both
So what does than make k? k is a^2 = 6.
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