document.write( "Question 222398: What is the value of the discriminant?
\n" ); document.write( "3x^2+10x-7=0
\n" ); document.write( "Also, what is the nature of the solutions? Are there 2 real solutions, 1 real solution, or 2 imaginary solutions? \n" ); document.write( "

Algebra.Com's Answer #166551 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "

Solved by pluggable solver: Computing the Discriminant

From $\"3x%5E2%2B10x-7\"$ we can see that $\"a=3\"$ , $\"b=10\"$ , and $\"c=-7\"$

$\"D=b%5E2-4ac\"$ Start with the discriminant formula.

$\"D=%2810%29%5E2-4%283%29%28-7%29\"$ Plug in $\"a=3\"$ , $\"b=10\"$ , and $\"c=-7\"$

$\"D=100-4%283%29%28-7%29\"$ Square $\"10\"$ to get $\"100\"$

$\"D=100--84\"$ Multiply $\"4%283%29%28-7%29\"$ to get $\"%2812%29%28-7%29=-84\"$

$\"D=100%2B84\"$ Rewrite $\"D=100--84\"$ as $\"D=100%2B84\"$

$\"D=184\"$ Add $\"100\"$ to $\"84\"$ to get $\"184\"$

Since the discriminant is greater than zero, this means that there are two real solutions.

\n" ); document.write( " \n" ); document.write( "

\n" );