document.write( "Question 7117: Use the discriminant to determine how many real-number roots the equation has. Do not solve the equation.
\n" ); document.write( "x^2-3x+5=0\r
\n" ); document.write( "\n" ); document.write( "That's what the worksheet says but I have no idea what a discriminant is or how to use it to determine how many real-number roots the equation has. What are real-number roots? Thank you to the tutors who help me with this. \n" ); document.write( "
Algebra.Com's Answer #3893 by Earlsdon(6294)\"\" \"About 
You can put this solution on YOUR website!
Perhaps a little review is in order.\r
\n" ); document.write( "\n" ); document.write( "One of the ways to solve quadratic equations is by employing the \"quadratic formula\":
\n" ); document.write( "\"x+=+%28-b+%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"\r
\n" ); document.write( "\n" ); document.write( "To use this formula however, the quadratic equation must be in \"standard form\":
\n" ); document.write( "\"ax%5E2+%2B+bx+%2B+c+=+0\"\r
\n" ); document.write( "\n" ); document.write( "Your equation is already in standard form.\r
\n" ); document.write( "\n" ); document.write( "What is the discriminant? It's that part of the quadratic formula under the square root sign: \"b%5E2+-+4ac\"\r
\n" ); document.write( "\n" ); document.write( "If the discriminant is positive, the solution has two real roots.
\n" ); document.write( "If the discriminant is negative, the solution has two complex conjugate roots.
\n" ); document.write( "If the discriminant is zero, the solution has one real root, but this is really a double root.\r
\n" ); document.write( "\n" ); document.write( "Let's look at the discriminant of your equation, \"x%5E2+-+3x+%2B+5+=+0\"\r
\n" ); document.write( "\n" ); document.write( "The discriminant is: \"%28-3%29%5E2+-+4%2A1%2A5+=+9+-+20\" = -11\r
\n" ); document.write( "\n" ); document.write( "The discriminant is negative, so the solution has two complex conjugate roots. \r
\n" ); document.write( "\n" ); document.write( "To interpret this result graphically, the parabola represented by your quadratic equation opens upwards (coefficient of x^2 is positive) and the parabola does not cross the x-axis. See the graph below:\r
\n" ); document.write( "\n" ); document.write( "\"graph%28300%2C200%2C-5%2C5%2C-2%2C10%2Cx%5E2-3x%2B5%29\"\r
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