document.write( "Question 262987: what value of k will make 16x^2/9 (fraction) - kx + 36 a perfect square trinomial? \n" ); document.write( "

Algebra.Com's Answer #853982 by ikleyn(53749) $\"\"$ $\"About$

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\n" ); document.write( "what value of k will make 16x^2/9 (fraction) - kx + 36 a perfect square trinomial?
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\n" ); document.write( "\n" ); document.write( " The post by @mananth gives incorrect answer to the problem's question.\r
\n" ); document.write( "\n" ); document.write( " See my solution below for correct, complete and clear solution.\r
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document.write( "I will give you / (show you) two ways to solve the problem, for your benefits.\r\n" );
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document.write( "            S o l u t i o n   1 \r\n" );
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document.write( "Your trinomial has a form  a^2*x^2 - kx + 36,  where  a^2 = ,  a =  = .\r\n" );
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document.write( "It will be a complete square if and only if \r\n" );
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document.write( "    k = +/-  = +/-  = +/- (2*4*2) = +/- 16.    <<<---===  ANSWER\r\n" );
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document.write( "            S o l u t i o n   2 \r\n" );
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document.write( "Consider the discriminant of the given polynomial \r\n" );
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document.write( "    d = \" b^2 - 4ac \",   where  b = -k,  a = ,  c = 36.\r\n" );
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document.write( "So,  d = (-k)^2 - 4*(16/9)*36 = k^2 - 16^2.\r\n" );
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document.write( "The given polynomial is a perfect square if and only if the discriminant is zero\r\n" );
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document.write( "    k^2 = 16^2,  which  implies  k = +/- 16.\r\n" );
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document.write( "You get the same answer as in Solution 1 above.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly and completely, in clear and transparent form.\r
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