document.write( "Question 155038: for what value(s) of p does the equation x^2+px+1=0 have no real solutions, and two real solutions. \n" ); document.write( "

Algebra.Com's Answer #114138 by Fombitz(32388) $\"\"$ $\"About$

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For this discussion, we'll use the discriminant.
\n" ); document.write( "For the general quadratic equation,
\n" ); document.write( " $\"ax%5E2%2Bbx%2Bc=0\"$
\n" ); document.write( "the discriminant is
\n" ); document.write( " $\"D=b%5E2-4ac\"$
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\n" ); document.write( "If $\"D%3E0\"$ then you have two distinct real roots.
\n" ); document.write( "If $\"D=0\"$ , you have a double root, one real root occurring twice
\n" ); document.write( "If $\"D%3C0\"$ , you have two complex roots, that are complex conjugates.\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bpx%2B1=0\"$
\n" ); document.write( " $\"D=p%5E2-4%281%29%281%29\"$
\n" ); document.write( " $\"D=p%5E2-4\"$
\n" ); document.write( "For no real (complex) solutions,
\n" ); document.write( " $\"D%3C0\"$
\n" ); document.write( " $\"p%5E2-4%3C0\"$
\n" ); document.write( " $\"p%5E2%3C4\"$
\n" ); document.write( "Valid interval: ( $\"-2%3Cp%3C2\"$ )
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\n" ); document.write( "For two real solutions,
\n" ); document.write( " $\"D%3E=0\"$
\n" ); document.write( " $\"p%5E2%3E=0\"$
\n" ); document.write( " $\"p%3E=2\"$ and $\"p%3C=-2\"$
\n" ); document.write( "Valid interval:( $\"-infinity\"$ , $\"-2\"$ ]U[ $\"2\"$ , $\"infinity\"$ ) \n" ); document.write( "

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