document.write( "Question 154861: Please help me:\r
\n" ); document.write( "\n" ); document.write( "1. How many solutions exist for a quadratic equation? How do we detemine whether the solutions are real or complex? \n" ); document.write( "

Algebra.Com's Answer #114026 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
In general, the number of solutions for a polynomial is equal to the degree of the polynomial.
\n" ); document.write( "A quadratic equation is a polynomial of degree 2 so it would have 2 solutions. The type of solutions a quadratic equation can be determined by examining the discriminant: $\"%28b%5E2-4ac%29\"$ which is taken from the quadratic formula: $\"x+=+-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"$
\n" ); document.write( "If the discriminant is negative, there are no real solutions/roots. This makes sense when you realize that a negative discriminant (the square root of a negative quantity) will yield complex solutions.
\n" ); document.write( "If the discriminant is zero, there is one real solution/root, sometimes referred to as a double root because you get two real solutions that are identical.
\n" ); document.write( "If the discriminant is positive, there are two real solutions/roots.
\n" ); document.write( "It is helpful to look at the graphs of quadratic equations with the above type of solutions/roots:\r
\n" ); document.write( "\n" ); document.write( " $\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C2x%5E2%2Bx%2B3%2Cx%5E2%2B6x%2B9%2Cx%5E2-5x%2B2%29\"$
\n" ); document.write( "Green graph: $\"y+=+2x%5E2%2Bx%2B3\"$ Discriminant is negative, no real roots.
\n" ); document.write( "Red graph: $\"y+=+x%5E2%2B6x%2B9\"$ Discriminant is zero, one double root.
\n" ); document.write( "Blue graph: $\"y+=+x%5E2-5x%2B2\"$ Discriminant is positive, two real root.
\n" ); document.write( "As you can see, the roots or solutions to these equations are the x-values where the curves (parabolas) intersect the x-axis. \n" ); document.write( "

\n" );