SOLUTION: what are the zeros for the polynomial 6x2 - 27x -54

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Question 273640: what are the zeros for the polynomial 6x2 - 27x -54
Found 2 solutions by asuar010, checkley77:
Answer by asuar010(338) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B-27x%2B-54+=+0) has the following solutons:

x%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=%28-27%29%5E2-4%2A6%2A-54=2025.

Discriminant d=2025 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--27%2B-sqrt%28+2025+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-27%29%2Bsqrt%28+2025+%29%29%2F2%5C6+=+6
x%5B2%5D+=+%28-%28-27%29-sqrt%28+2025+%29%29%2F2%5C6+=+-1.5

Quadratic expression 6x%5E2%2B-27x%2B-54 can be factored:
6x%5E2%2B-27x%2B-54+=+6%28x-6%29%2A%28x--1.5%29
Again, the answer is: 6, -1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-27%2Ax%2B-54+%29

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
6x2 - 27x -54=0
(6x+9)(x-6)=0
6x+9=0
6x=-9
x=-9/6
x=-1.5 ans.
x-6=0
x=6 ans.