SOLUTION: 32. Find all real or imaginary solutions. 9y^2 + 16 = 0 36. Show a complete solution. Two positive number differ by 11, and their square roots differ by 1. Find the numbe

Algebra ->  Algebra  -> Radicals -> SOLUTION: 32. Find all real or imaginary solutions. 9y^2 + 16 = 0 36. Show a complete solution. Two positive number differ by 11, and their square roots differ by 1. Find the numbe      Log On

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Question 38556: 32. Find all real or imaginary solutions.
9y^2 + 16 = 0
36. Show a complete solution.
Two positive number differ by 11, and their square roots differ by 1. Find the numbers.

Answer by lyra(94) About Me  (Show Source):
You can put this solution on YOUR website!
Please only put one problem in each submission, I will solve the first one.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 9y%5E2%2B0y%2B16+=+0) has the following solutons:

y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280%29%5E2-4%2A9%2A16=-576.

The discriminant -576 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -576 is + or - sqrt%28+576%29+=+24.

The solution is y%5B12%5D+=+%28-0%2B-+i%2Asqrt%28+-576+%29%29%2F2%5C9+=++%28-0%2B-+i%2A24%29%2F2%5C9+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B0%2Ax%2B16+%29


Hope this helps and feel free to contact me with further questions,
lyra