document.write( "Question 157288This question is from textbook elementary and intermediate algebra
\n" ); document.write( ": How do I find the discriminant? The question ask to find $\"b%5E2-4ac\"$ and the number of real solutions to each equation.
\n" ); document.write( "35. $\"4m%5E2%2B25+=+20m\"$
\n" ); document.write( "45. $\"x%5E2=x\"$ \n" ); document.write( "

Algebra.Com's Answer #115914 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!
How do I find the discriminant? The question ask to find $\"b%5E2-4ac\"$ and the number of real solutions to each equation.
\n" ); document.write( "35. $\"4m%5E2%2B25+=+20m\"$
\n" ); document.write( "45. $\"x%5E2=x\"$ \r
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document.write( "You must first rearrange the equations so that 0 appears\r\n" );
document.write( "on the right and the three terms on the left are in \r\n" );
document.write( "descending order like this:\r\n" );
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document.write( ",  or whatever \r\n" );
document.write( "the letter of the unknown happens to be:\r\n" );
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document.write( "That's the only way you can tell what to substitute for\r\n" );
document.write( ", , and  in the formula:\r\n" );
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document.write( "For your problem 35:\r\n" );
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document.write( "You must first get a 0 on the right side by adding  to\r\n" );
document.write( "both sides:\r\n" );
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document.write( "And you must write the left side in descending order, like \r\n" );
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document.write( "Then when you compare that to\r\n" );
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document.write( "it is easy to see that ,, and .\r\n" );
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document.write( "So then you can easily substitute those values in the \r\n" );
document.write( "expression for the discriminant:\r\n" );
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document.write( "When the discriminant is 0, there is \r\n" );
document.write( "exactly 1 real solution. So this particular\r\n" );
document.write( "quadratic equation has 1 real solution.\r\n" );
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document.write( "If it were negative there would be no real solutions,\r\n" );
document.write( "and if it were positive there would be exactly two real\r\n" );
document.write( "solutions.\r\n" );
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document.write( "For your problem 45:\r\n" );
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document.write( "You must first get a 0 on the right side by adding  to\r\n" );
document.write( "both sides:\r\n" );
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document.write( "But the left side contains only two terms! So you must \r\n" );
document.write( "add on a  to the left side:\r\n" );
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document.write( "Also it may be helpful to write the understood 's before\r\n" );
document.write( " and , like this:\r\n" );
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document.write( "The left side is already in descending order, so when you \r\n" );
document.write( "compare that to\r\n" );
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document.write( ", \r\n" );
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document.write( "it is easy to see that ,, and .\r\n" );
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document.write( "So then you can easily substitute those values in the \r\n" );
document.write( "expression for the discriminant:\r\n" );
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document.write( "Since the discriminant is a positive number,\r\n" );
document.write( "there are exactly two real solutions.\r\n" );
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document.write( "Edwin

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