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

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Question 1179332: Find the values of k such that 4x^2+16x+k has the following solution.
a. two real number solutions
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. two real number solutions
it will be if discriminant b%5E2-4ac%3E0
4x%5E2%2B16x%2Bk...in this case a=4, b=16, and c=k
16%5E2-4%2A4%2Ak%3E0
16%5E2-16k%3E0
16%2816-k%29%3E0
will be equal to zero if 16-k%3E0->16%3Ek or k%3C16
let try k=15
4x%5E2%2B16x%2B15
and real solution is
4x%5E2%2B16x%2B15=0 use quadratic formula
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29............a=4, b=16, and c=15
x=%28-16%2B-sqrt%2816%5E2-4%2A4%2A15%29%29%2F%282%2A4%29
x=%28-16%2B-sqrt%2816%29%29%2F8
x=%28-16%2B-4%29%2F8
x=%28-4%2B-1%29%2F2
x=-3%2F2
or
x=-5%2F2
see the graph below:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C4x%5E2%2B16x%2B15%29+