document.write( "Question 1106233: determine all possible values of k so that the quadratic below has one zero.
\n" ); document.write( "x^2 + (k-5)x + (4-5k) = 0\r
\n" ); document.write( "\n" ); document.write( "the asnwers are k = -1 and k = -9. thank you! \n" ); document.write( "

Algebra.Com's Answer #721177 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "A quadratic equation   ax^2 + bx + c = 0\r\n" );
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document.write( "    - has two real zeroes if and only if the discriminant d = b^2 - 4ac is POSITIVE;\r\n" );
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document.write( "    - has one real zero   if and only if the discriminant d = b^2 - 4ac is ZERO;\r\n" );
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document.write( "    - has NO real zeroes if and only if the discriminant d = b^2 - 4ac is NEGATIVE.\r\n" );
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document.write( "So, for your equation, in order for the condition was satisfied, the discriminant \r\n" );
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document.write( "(k-5)^2 - 4*(4-5k)  must be equal to zero:\r\n" );
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document.write( "(k-5)^2 - 4*(4-5k) = 0.\r\n" );
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document.write( "It is your equation to find the values of \"k\".\r\n" );
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document.write( "Simplify and solve it by any method you know.\r\n" );
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\n" ); document.write( "If you still have questions, you can post them to me through the \"Thank you\" window/form.\r
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\n" ); document.write( "\n" ); document.write( "In his case refer to the problem ID number 1106233.\r
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\n" ); document.write( "\n" ); document.write( "I will help you free of charge.\r
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