document.write( "Question 844058: Find the smallest integral value of c that will produce imaginary roots in the equation: 4x^2-7x+c=0 \n" ); document.write( "

Algebra.Com's Answer #508504 by Fombitz(32388) $\"\"$ $\"About$

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Look at the discriminant, $\"D=b%5E2-4ac\"$
\n" ); document.write( " $\"D=%28-7%29%5E2-4%284%29%28c%29\"$
\n" ); document.write( " $\"D=49-16c\"$
\n" ); document.write( "For complex roots, the discriminant is negative.
\n" ); document.write( " $\"49-16c%3C0\"$
\n" ); document.write( " $\"-16c%3C-49\"$
\n" ); document.write( " $\"c%3E49%2F16\"$
\n" ); document.write( " $\"48%2F16=3\"$ so the next integer value is $\"c=4\"$
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\n" ); document.write( " $\"graph%28300%2C300%2C-1%2C4%2C-1%2C4%2C4x%5E2-7x%2B3%2C4x%5E2-7x%2B4%29\"$
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\n" ); document.write( "Shown are graphs of $\"4x%5E2-7x%2B3\"$ (Red) with real roots and $\"4x%5E2-7x%2B4\"$ (Green) with no real roots. \n" ); document.write( "

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