document.write( "Question 1099436: The cubic equation x^3-12x^2+ax-48=0 has roots p,2p and 3p. Find the value of p.
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Algebra.Com's Answer #713862 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "According to Vieta's theorem, the product of the roots is equal to the constant term taken with the opposite sign in this case.\r\n" );
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document.write( "In the mathematical form,  p*(2p)*(3p) = 48,   or\r\n" );
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document.write( "6p^3 = 48  ====>  p^3 =  = 8  ====>  p =  = 2.\r\n" );
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document.write( "Answer.  p = 2.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is INTERESTING that under the given condition, the answer DOES NO DEPEND on the value of the coefficient \"a\" of the given equation.\r
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document.write( "    In opposite, by knowing all the roots p= 2, 2p = 4  and  3p= 6, we can calculate the coefficient \"a\" \r\n" );
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document.write( "    (using again the Vieta's theorem) as the sum of all pair-wise products of the roots:\r\n" );
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document.write( "    a = 2*4 + 2*6 + 4*6 = 8 + 12 + 24 = 44.\r\n" );
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