document.write( "Question 736470: Without solving, determine the character of the solutions of each equation in the complex number system.\r
\n" ); document.write( "\n" ); document.write( "4x^2 + 12x + 9 =0 \n" ); document.write( "

Algebra.Com's Answer #449844 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
In the quadratic formula for finding roots,
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$ , the
\n" ); document.write( "discriminant is $\"++b%5E2-4%2Aa%2Ac+\"$
\n" ); document.write( "This determines the types of solutions
\n" ); document.write( " $\"+4x%5E2+%2B+12x+%2B+9+=0+\"$
\n" ); document.write( " $\"+a+=+4+\"$
\n" ); document.write( " $\"+b+=+12+\"$
\n" ); document.write( " $\"+c+=+9+\"$
\n" ); document.write( " $\"+b%5E2+-+4%2Aa%2Ac+=+12%5E2+-+4%2A4%2A9+\"$
\n" ); document.write( " $\"+b%5E2+-+4%2Aa%2Ac+=+144+-+144+\"$
\n" ); document.write( "----------------
\n" ); document.write( "The discriminant is $\"+0+\"$ , so there is a single solution,
\n" ); document.write( "called a double root $\"+x+=+-b%2F%282a%29+\"$
\n" ); document.write( "Here's the plot:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-4%2C+2%2C+-2%2C+10%2C+4x%5E2+%2B+12x+%2B+9+%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );