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 #721176 by Boreal(15235) $\"\"$ $\"About$

You can put this solution on YOUR website!
This needs completing the square, since that would give one zero with multiplicity 2. This is done by taking the coefficient of the x term, dividing it by 2 and squaring it. That will give the coefficient of the constant.
\n" ); document.write( "Here, those values are:
\n" ); document.write( "[(1/2)(k-5)]^2=(4-5k)
\n" ); document.write( "(1/4)(k^2-10k+25)=(4-5k)
\n" ); document.write( "k^2-10k+25=16-20k, multiplying by 4
\n" ); document.write( "k^2+10k+9=0
\n" ); document.write( "(k+9)(k+1)=0
\n" ); document.write( "k=-9 and -1 \n" ); document.write( "

\n" );