SOLUTION: Please help me solve this function, " Find the zeros of the function f(x)=x^2+6x+18 "

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Question 762666: Please help me solve this function, " Find the zeros of the function f(x)=x^2+6x+18 "
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Given: 0+=+X%5E2+%2B+6X+%2B+18
You can use the quadratic equation to solve for X.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aX%5E2%2BbX%2Bc=0 (in our case 1X%5E2%2B6X%2B18+=+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=%286%29%5E2-4%2A1%2A18=-36.

The discriminant -36 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 -36 is + or - sqrt%28+36%29+=+6.

The solution is X%5B12%5D+=+%28-6%2B-+i%2Asqrt%28+-36+%29%29%2F2%5C1+=++%28-6%2B-+i%2A6%29%2F2%5C1+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B18+%29

Since the discriminant is less than 0, there are no solutions without using imaginary numbers. This is why the graph never touches the X-axis.