Question 1209248
<pre>

{{{2x^2 + 3x - 20x + 3x^2 + k}}}

{{{5x^2 - 17x + k}}}

It will have a double root if its discriminant b<sup>2</sup>-4ac = 0

{{{discriminant = (-17)^2-4(5)(k) = 0}}}
{{{289-20k = 0}}}
{{{-20k=-289}}}
{{{k=(-289)/(-20)}}}
{{{k=289/20}}}    <-- answer

Checking:
{{{2x^2 + 3x - 20x + 3x^2 + 289/20=0}}}
{{{5x^2 - 17x + 289/20=0}}}
{{{100x^2-340x+289=0}}}
{{{(10x-17)(10x-17)=0}}}
10x-17=0;  10x-17=0
   10x=17;    10x=17
     x={{{17/10}}};     x={{{17/10}}}

So both roots are the same, so it has a double root if {{{k=289/20}}}

So {{{k=289/20}}} is correct.

Edwin</pre>