document.write( "Question 330626: 1. How many solutions exist for a quadratic equation? Explain and example
\n" ); document.write( "2. How do we determine whether the solutions are real or complex? Example.
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Algebra.Com's Answer #237019 by Fombitz(32388)\"\" \"About 
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1.There are always two solutions to a quadratic equation.
\n" ); document.write( "They may be a complex conjugate pair solution or a real solution, which includes the possibility of a double root at one x value.
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\n" ); document.write( "2. Graphically, you can graph the function and see if it ever crosses the x axis. If it does, then the roots are real, if not, then the roots are complex.
\n" ); document.write( "Algebraically, use the discriminant,
\n" ); document.write( "\"D=b%5E2-4ac\" where the quadratic equation is in the form \"ax%5E2%2Bbx%2Bc=0\".
\n" ); document.write( "If \"D%3E0\", two real distinct roots.
\n" ); document.write( "If \"D=0\", one real double root.
\n" ); document.write( "If \"D%3C0\", two complex conjugate pair roots.
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\n" ); document.write( "\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2%2B3x-10%2C%28x-5%29%5E2%2Cx%5E2%2Bx%2B2%29\"
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\n" ); document.write( "The red curve has two real roots, \"y=x%5E2%2B3x-10\", \"D=9%2B40=49\"
\n" ); document.write( "The green curve has one real double root, \"y=x%5E2-10x%2B25\",\"D=100-100=0\"
\n" ); document.write( "The blue curve has complex conjugate roots, \"y=x%5E2%2Bx%2B2\",\"D=1-8=-7\" \n" ); document.write( "
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