document.write( "Question 1205171: If 𝛼, 𝛽, 𝛾 (where 𝛼, 𝛽, 𝛾 ≠ 0) are the roots of the equation 𝑥
\n" ); document.write( "3 + 𝑝𝑥^2 + 𝑞𝑥 + 𝑟 = 0, where 𝑝, 𝑞
\n" ); document.write( "and 𝑟 (≠ 0) are real numbers, express the following in terms of 𝑝, 𝑞 and 𝑟:
\n" ); document.write( "𝛼^2𝛽^2 + 𝛽^2𝛾^2 + 𝛼^2𝛾^2 \n" ); document.write( "

Algebra.Com's Answer #842163 by Bogz(13) $\"\"$ $\"About$

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If $\"alpha\"$ , $\"beta\"$ , $\"gamma\"$ are the roots of $\"x%5E3%2Bpx%5E2+%2B+qx+%2Br+=+0\"$ , then we know that \r
\n" ); document.write( "\n" ); document.write( " $\"alpha+%2B+beta+%2B+gamma+=+-p\"$ ,
\n" ); document.write( " $\"alpha%2Abeta+%2B+beta%2Agamma+%2B+alpha%2Agamma+=+q\"$ , and
\n" ); document.write( " $\"alpha%2Abeta%2Agamma+=+-r\"$ .\r
\n" ); document.write( "\n" ); document.write( "The 2nd equation above gives
\n" ); document.write( " $\"%28alpha%2Abeta+%2B+beta%2Agamma+%2B+alpha%2Agamma%29%5E2+=+q%5E2\"$ .\r
\n" ); document.write( "\n" ); document.write( "But the left side of the preceding equation expands to \r
\n" ); document.write( "\n" ); document.write( "

.\r
\n" ); document.write( "\n" ); document.write( "Hence,

.\r
\n" ); document.write( "\n" ); document.write( "Therefore,

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\n" );