document.write( "Question 823037: 5x^2-6x-h=0
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Algebra.Com's Answer #495224 by rothauserc(4718) $\"\"$ $\"About$

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first look at the discriminant of this quadratic equation
\n" ); document.write( "5x^2-6x-h=0, which is
\n" ); document.write( "b^2 - 4*a*c, now substitute what we know
\n" ); document.write( "(-6)^2 - 4*5*(-h)
\n" ); document.write( "36+20*h
\n" ); document.write( "now is there a value of h that gives us a rational square root?
\n" ); document.write( "if h = 8, then we have
\n" ); document.write( "square root of (36+20*8) is 14 and using quadratic formula
\n" ); document.write( "x = (-(-6) + 14) / (2*5) = 2
\n" ); document.write( "x = (-(-6) - 14) / (2*5) = -4/5
\n" ); document.write( "now we have
\n" ); document.write( "5x^2 -6x -8 = 0
\n" ); document.write( "if x = 2, then
\n" ); document.write( "5*2^2 -6*2 -8 = 0
\n" ); document.write( "20 -12 -8 = 0
\n" ); document.write( "0 = 0
\n" ); document.write( "x = 2 checks
\n" ); document.write( "now try -4/5
\n" ); document.write( "5*(-4/5)^2 -6*(-4/5) -8 = 0
\n" ); document.write( "16/5 + 24/5 -8 = 0
\n" ); document.write( "40/5 -8 = 0
\n" ); document.write( "8 -8 = 0
\n" ); document.write( "answer checks
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