document.write( "Question 1136528: If z=3 is a solution of the equation 5z^2+kz-30=0 the value of k and other solution of the equation are respectively
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Algebra.Com's Answer #754326 by ikleyn(52814) $\"\"$ $\"About$

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document.write( "The given equation is equivalent to quadratic equation\r\n" );
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document.write( "     = 0     (1)\r\n" );
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document.write( "with the leading coefficient 1.  (Notice that equation (1) is obtained from the given equation by division all the terms by 5.)\r\n" );
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document.write( "Therefore, equation (1) has the root z= 3.\r\n" );
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document.write( "According to Vieta's theorem, the product of the roots of the equation (1) is equal to its constant term, which is -6.\r\n" );
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document.write( "Therefore, the second root of the equation (1) is   = -2.\r\n" );
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document.write( "Thus the two roots of the equation (1) are 3 and -2.\r\n" );
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document.write( "Then, according to the Vieta's theorem, the sum of its roots (which is  3+(-2) = 1) is equal to the coefficient at x with the opposite sign.\r\n" );
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document.write( "In other words,   = 3+(-2) = 1,  which implies  k = -5.\r\n" );
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document.write( "ANSWER.  The second root of the given equation is -2 and k= -5.\r\n" );
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