document.write( "Question 1142263: Given that x²+bx+18 is factorised as (x+2)(x+c). Find the values of c and b \n" ); document.write( "

Algebra.Com's Answer #762957 by ikleyn(52779) $\"\"$ $\"About$

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document.write( "Since x^2 + bx + 18 is factored as (x+2)*(x+c), it means that x= -2 is the root of the polynomial x^2 + bx + 18 :\r\n" );
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document.write( "    (-2)^2 + b*(-2) + 18 = 0,\r\n" );
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document.write( "    4       -2b     + 18 = 0,\r\n" );
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document.write( "    4 + 18 = 2b  ====>  2b = 22  ====>  b = 11.\r\n" );
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document.write( "Next, according to Vieta's theorem, the constant term 18 of the polynomial x^2 + bx + 18  is the product of its roots.\r\n" );
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document.write( "One of the root is x= -2.  Hence, the other root is   = -9.\r\n" );
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document.write( "From the other side, the other root is x= -c.  \r\n" );
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document.write( "Hence,  c= 9.\r\n" );
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document.write( "ANSWER.  b = 11;  c = 9.\r\n" );
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