Question 988562
Finish the description correctly.  "...when the root of the EXPRESSION is repeated."


The variable being x,  Use the discriminant.


{{{kx^2+(k+1)x-(k+2)=0}}} for the equation.
Discriminant must also be zero,  {{{(k+1)^2-4*k(-1)(k+2)=0}}}.


{{{(k+1)^2+4k(k+2)=0}}}
{{{k^2+2k+1+4k^2+8k=0}}}
{{{5k^2+10k+1=0}}}
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{{{k=(-10+- 4sqrt(5))/(2*5)}}}
{{{highlight(k=(-5+- 2sqrt(5))/5)}}}