document.write( "Question 696524: in a quadratic equation x^2 + px + q =0 if sum of its roots are equal to thrice of their difference then proove that
\n" ); document.write( "2p^2 = 9q \n" ); document.write( "
Algebra.Com's Answer #429074 by stanbon(75887)\"\" \"About 
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in a quadratic equation x^2 + px + q =0 if sum of its roots are equal to thrice of their difference then prove that 2p^2 = 9q
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\n" ); document.write( "Roots:
\n" ); document.write( "[-p+sqrt(p^2-4q)]/(2)
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\n" ); document.write( "[-p-sqrt(p^2-4q)]/(2)\r
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\n" ); document.write( "Sum: -p/2+-p/2 = -p
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\n" ); document.write( "Diff: sqrt(p^2-4q)
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\n" ); document.write( "Equation:
\n" ); document.write( "sum = 3*diff
\n" ); document.write( "-p = 3[sqrt(p^2-4q)]
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\n" ); document.write( "sqrt(p^2-4q) = -p/3
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\n" ); document.write( "Square both sides to get:
\n" ); document.write( "p^2 - 4q = p^2/9
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\n" ); document.write( "9p^2 - 36q = p^2
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\n" ); document.write( "8p^2 = 36q
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\n" ); document.write( "2p^2 = 9q
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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