document.write( "Question 1100749: Find all roots of \"k\" such that 2x^2-kx+2=0 has one real root \n" ); document.write( "

Algebra.Com's Answer #715292 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "The discriminant, which is b²-4ac, must be zero in \r\n" );
document.write( "order for this equation to have just one real root:\r\n" );
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document.write( "So we set this discriminant equal to zero:\r\n" );
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document.write( "Solve that either of two ways:\r\n" );
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document.write( "First way:\r\n" );
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document.write( "Add 16 to both sides:\r\n" );
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document.write( "Use the principle of square roots:\r\n" );
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document.write( "   <-- the answers \r\n" );
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document.write( "Second way:\r\n" );
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document.write( "Factor the left side as the difference of two squares:\r\n" );
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document.write( "k-4 = 0;  k+4 = 0\r\n" );
document.write( "  k = 4;    k = -4   <-- the answers\r\n" );
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document.write( "-------\r\n" );
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document.write( "To prove that  just has one\r\n" );
document.write( "real root when k = 4 or k = -4, we substitute in\r\n" );
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document.write( "Substituting 4 for k:\r\n" );
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document.write( "Divide both sides by 2\r\n" );
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document.write( "Factor:\r\n" );
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document.write( "x-1 = 0; x-1 = 0\r\n" );
document.write( "  x = 1   x = 1   <-- just 1 root, 1\r\n" );
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document.write( "---\r\n" );
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document.write( "Substituting -4 for k:\r\n" );
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document.write( "Divide both sides by 2\r\n" );
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document.write( "Factor:\r\n" );
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document.write( "x+1 = 0;  x+1 = 0\r\n" );
document.write( "  x = -1    x = -1   <-- just 1 root, -1\r\n" );
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document.write( "Edwin

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