document.write( "Question 8627: What is the value of the discriminant and also the nature of the roots of the equation $\"5n%5E2=4n%2B6\"$ \n" ); document.write( "

Algebra.Com's Answer #4789 by glabow(165) $\"\"$ $\"About$

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The discriminant is the value $\"sqrt%28b%5E2+-+4ac%29\"$ where a, b, and c are the coefficients of the quadratic equation in the standard form $\"ax%5E2%2Bbx%2Bc\"$ .
\n" ); document.write( "This means you want to first rearrange the equation you have to standard form.
\n" ); document.write( " $\"5n%5E2=4n%2B6\"$
\n" ); document.write( " $\"5n%5E2+-4n-6=0\"$ [adding -4n-6 to both sides]
\n" ); document.write( "So, a=5, b=-4, and c=-6
\n" ); document.write( "The discriminant is $\"sqrt%28%28%28-4%29%28-4%29%29+-+%28%284%29%285%29%28-6%29%29%29\"$
\n" ); document.write( "which is $\"sqrt%2816%2B120%29=sqrt%28136%29=11.66\"$ or so.\r
\n" ); document.write( "\n" ); document.write( "This tells you that the solutions of the equation are both real.
\n" ); document.write( "This is clear also from the graph of the equation
\n" ); document.write( " $\"graph%28500%2C+500%2C+-5%2C+5%2C+-10%2C+10%2C+5x%5E2-4x-6%29\"$
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