document.write( "Question 972973: If α(alpha) and β (beta) are the roots of the equation ax^2+bx+c,then the value of α^3+ β ^3 is: \n" ); document.write( "

Algebra.Com's Answer #595240 by reviewermath(1029) $\"\"$ $\"About$

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If α(alpha) and β (beta) are the roots of the equation ax^2+bx+c,then the value of α^3+ β ^3 is:
\n" ); document.write( "Solution:
\n" ); document.write( "The sum of the roots of the equation $\"ax%5E2%2Bbx%2Bc+=+0\"$ is $\"-b%2Fa\"$ and the product of the roots is $\"c%2Fa\"$ .
\n" ); document.write( " $\"%28alpha%29%5E3+%2B+%28beta%29%5E3\"$ = $\"%28%28alpha%29%2B%28beta%29%29%28%28alpha%29%5E2-%28alpha%29%28beta%29%2B%28beta%29%5E2%29\"$ = $\"%28-b%2Fa%29%28%28alpha%29%5E2%2B%28beta%29%5E2-c%2Fa%29\"$
\n" ); document.write( "But $\"%28alpha%29%5E2%2B%28beta%29%5E2\"$ = $\"%28%28alpha%29+%2B+%28beta%29%29%5E2+-+2%28alpha%29%28beta%29\"$
\n" ); document.write( "= $\"%28-b%2Fa%29%5E2+-+2%28c%2Fa%29\"$
\n" ); document.write( "Therefore,
\n" ); document.write( " $\"%28alpha%29%5E3+%2B+%28beta%29%5E3\"$ = $\"%28-b%2Fa%29%28%28-b%2Fa%29%5E2+-+2%28c%2Fa%29-c%2Fa%29\"$
\n" ); document.write( "= $\"highlight%28%28-b%2Fa%29%28%28-b%2Fa%29%5E2+-+3%28c%2Fa%29%29%29\"$ \n" ); document.write( "

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