SOLUTION: If the two solutions of the quadratic equation 4x^2+4x+k=0 are equal, find k I would greatly appreciate the help. Thank you

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: If the two solutions of the quadratic equation 4x^2+4x+k=0 are equal, find k I would greatly appreciate the help. Thank you      Log On


   

Question 481964: If the two solutions of the quadratic equation 4x^2+4x+k=0 are equal, find k
I would greatly appreciate the help. Thank you
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: If the two solutions are equal, this essentially means you have one solution. Recall that the equation ax%5E2%2Bbx%2Bc=0 has one solution when b%5E2-4ac=0

So what this means is that because 4x%5E2%2B4x%2Bk=0 has one solution, we know that 4%5E2-4%284%29%28k%29=0 (note: a=4, b=4, and c=k). Solve this equation for k to find your answer.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If the two solutions of the quadratic equation 4x^2+4x+k=0 are equal, find k
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For the solutions to be equal the quadratic must be perfect square.
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The discriminant must be zero:
b^2-4ac = 4^2 - 4*4*k = 0
16 - 16k = 0
k = 1
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Cheers,
Stan H.
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