SOLUTION: Find the values of k such that 4x^2+16x+k has the following solutions. a.exactly one real-number solution

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Question 1179333: Find the values of k such that 4x^2+16x+k has the following solutions.
a.exactly one real-number solution
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the values of k such that 4x%5E2%2B16x%2Bk has the following solutions.
a. exactly one real-number solution
it will be if discriminant b%5E2-4ac=0
4x%5E2%2B16x%2Bk...in this case a=4, b=16, and c=k
16%5E2-4%2A4%2Ak=0
16%5E2-16k=0
16%2816-k%29=0
will be equal to zero if 16-k=0->k=16

4x%5E2%2B16x%2B16
and real solution is
4x%5E2%2B16x%2B16=0.........factor
4%28x%5E2%2B2x%2B4%29=0
4%28x%2B2%29%5E2=0
=>x=-2 which is a point (-2,0)
see the graph below:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C4x%5E2%2B16x%2B16%29+