document.write( "Question 19276: $\"x%5E2-x-1=0\"$ I thought it had no real solution, but I guess I did it wrong. \n" ); document.write( "

Algebra.Com's Answer #9311 by Earlsdon(6294) $\"\"$ $\"About$

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The discriminant can be used to determine the nature of the solutions to the quadratic equation.
\n" ); document.write( "The discriminant is: $\"b%5E2+-+4ac\"$ this is just the part under the radical of the quadratic formula: $\"x+=+%28-b%2B-sqrt%28b%5E2+-+4ac%29%29%2F2a\"$ \r
\n" ); document.write( "\n" ); document.write( "If the discriminant is negative, the solutions are not real, you have two complex conjugate roots.
\n" ); document.write( "If the discriminant is positive, the two roots are real.
\n" ); document.write( "If the discriminant is zero, you have one real root (a double root)\r
\n" ); document.write( "\n" ); document.write( "Let's check the discriminant of your quadratic equation.\r
\n" ); document.write( "\n" ); document.write( " $\"%28-1%29%5E2+-+4%281%29%28-1%29\"$ = $\"1+%2B+4+=+5\"$ The disriminant is positive, therefore, there are two real roots. What are they?\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-%28-1%29%2B-sqrt%28%28-1%29%5E2+-+4%281%29%28-1%29%29%29%2F2%281%29\"$
\n" ); document.write( " $\"x+=+%281%2B-sqrt%285%29%29%2F2\"$
\n" ); document.write( " $\"x+=+%281%2F2%29+%2B+%281%2F2%29sqrt%285%29\"$ and/or $\"x+=+%281%2F2%29-%281%2F2%29sqrt%285%29\"$ \n" ); document.write( "

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