document.write( "Question 762666: Please help me solve this function, \" Find the zeros of the function f(x)=x^2+6x+18 \" \n" ); document.write( "
Algebra.Com's Answer #464091 by Stitch(470)\"\" \"About 
You can put this solution on YOUR website!
Given: \"0+=+X%5E2+%2B+6X+%2B+18\"
\n" ); document.write( "You can use the quadratic equation to solve for X.
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
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:
\n" ); document.write( "
\n" ); document.write( " \"X%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
\n" ); document.write( "
\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
\n" ); document.write( "
\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%286%29%5E2-4%2A1%2A18=-36\".
\n" ); document.write( "
\n" ); document.write( " The discriminant -36 is less than zero. That means that there are no solutions among real numbers.

\n" ); document.write( " If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

\n" ); document.write( "
\n" ); document.write( " In the field of imaginary numbers, the square root of -36 is + or - \"sqrt%28+36%29+=+6\".
\n" ); document.write( "
\n" ); document.write( " 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+\"
\n" ); document.write( "
\n" ); document.write( " Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B18+%29\"

\n" ); document.write( "\n" ); document.write( "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. \n" ); document.write( "
\n" );