document.write( "Question 512143: State the value of the discriminant and then describe the nature of the solutions. 19x^2-5x+4=0 \n" ); document.write( "

Algebra.Com's Answer #342547 by jim_thompson5910(35256) $\"\"$ $\"About$

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From $\"19x%5E2-5x%2B4\"$ we can see that $\"a=19\"$ , $\"b=-5\"$ , and $\"c=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"D=b%5E2-4ac\"$ Start with the discriminant formula.\r
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\n" ); document.write( "\n" ); document.write( " $\"D=%28-5%29%5E2-4%2819%29%284%29\"$ Plug in $\"a=19\"$ , $\"b=-5\"$ , and $\"c=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"D=25-4%2819%29%284%29\"$ Square $\"-5\"$ to get $\"25\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"D=25-304\"$ Multiply $\"4%2819%29%284%29\"$ to get $\"%2876%29%284%29=304\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"D=-279\"$ Subtract $\"304\"$ from $\"25\"$ to get $\"-279\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the discriminant is $\"D=-279\"$ \r
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\n" ); document.write( "\n" ); document.write( "Since the discriminant is less than zero, this means that there are two complex solutions.\r
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\n" ); document.write( "\n" ); document.write( "In other words, there are no real solutions.
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