document.write( "Question 1131744: Find the roots of the equation x³ - 9x² + 23x - 15 = 0, if they are in AP. \n" ); document.write( "

Algebra.Com's Answer #748440 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The given information that the roots are in AP makes the problem easy.

\n" ); document.write( "For the shortest path to the solution, use the rational roots theorem as suggested by tutor @josgarithmetic and Vieta's theorem as suggested by tutor @ikleyn:

\n" ); document.write( "(1) The possible rational roots are 1, 3, 5, -1, -3, and -5.
\n" ); document.write( "(2) The product of the roots is -(-15/1) = 15; the sum of the roots is -(-9)/1 = 9.

\n" ); document.write( "The only possible rational roots that satisfy Vieta's theorem are 1, 3, and 5.

\n" ); document.write( "ANSWER: The roots are 1, 3, and 5. \n" ); document.write( "

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