document.write( "Question 546238: x²+6=0 \r
\n" ); document.write( "\n" ); document.write( "Determine the nature of the solutions of the equation.\r
\n" ); document.write( "\n" ); document.write( "I need help please
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Algebra.Com's Answer #355941 by KMST(5328) $\"\"$ $\"About$

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For any $\"x\"$ that is a real number, $\"x%5E2%3E=0\"$ , so $\"x%5E2%2B6%3E=6\"$ .
\n" ); document.write( "As a consequence, no real number can be a solution of $\"x%5E2%2B6=0\"$ .
\n" ); document.write( "The solutions are complex numbers, imaginary numbers, and you could find them, if you know about complex numbers.
\n" ); document.write( "What you probably were expected to do, is calculate the discriminant.
\n" ); document.write( "All quadratic equations can be represented by the general form
\n" ); document.write( " $\"ax%5E2%2Bbx%2Bc=0\"$ with $\"a\"$ different from zero.
\n" ); document.write( "In your case $\"a=1\"$ , $\"b=0\"$ and $\"c=6\"$
\n" ); document.write( "The discriminant is the expression $\"b%5E2-4%2Aa%2Ac\"$ .
\n" ); document.write( "In your case $\"b%5E2-4%2Aa%2Ac=0%5E2-4%281%29%286%29=0-24=-24\"$ .
\n" ); document.write( "The textbooks tell you that if the discriminant is negative there are no real solutions, but there are two imaginary solutions.
\n" ); document.write( "(They also tell you that if the discriminant is zero, there is one real solution, and if it is positive, there are two real solutions). \n" ); document.write( "

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