document.write( "Question 232608: I am supposed to determine the nature of the solutions of the equation. Determine whther there is one real solution, two real solutions, or two non real solutions.\r
\n" ); document.write( "\n" ); document.write( "x^2 - 3x +8 =0\r
\n" ); document.write( "\n" ); document.write( "There is two real solutions? \n" ); document.write( "
Algebra.Com's Answer #171862 by jsmallt9(3758)\"\" \"About 
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The general form of a quadratic equation:
\n" ); document.write( "\"ax%5E2+%2B+bx++%2B+c+=+0\"
\n" ); document.write( "The quadratic formula:
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28b%5E2+-4ac%29%29%2F%282a%29\"

\n" ); document.write( "The expression inside the square root, \"b%5E2-4ac\", is called the discriminant. It is called this because its value determines whether there are 0, 1 or 2 real roots. This is how it works:
  • The discriminant is a positive number (any positive number. Since the discriminant is inside the square root we will find the square root of the discriminant. The square root of a positive number is another positive number. And since this square root is both added to and subtracted from -b in the numerator, we will end up with 2 real roots: one when we add the square root and one when we subtract.
  • The discriminant is zero. The square root of zero is zero. And whether you add zero to -b or subtract zero from -b you end up with the same thing, -b. This is when we get 1 real root.
  • The discriminant is a negative number (any negative number). Since it is impossible to square a real number and get a negative number, the square root of any negative number does not exist within the set of Real numbers. This is when we get no real roots.

\n" ); document.write( "Using this on you equation...
\n" ); document.write( "Find the value of the discriminant:
\n" ); document.write( "\"b%5E2+-+4ac+=+%28-3%29%5E2+-+4%281%29%288%29+=+9+-+32+=+-23\"
\n" ); document.write( "The discriminant is a negative number so there are no real roots. \n" ); document.write( "
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