Question 1067025
.
Show that there are no values of k for which the line y=3-2x can intersect the curve y=2x^2+kx+3
~~~~~~~~~~~~~~~~~~~~~~


The statement is WRONG.


The counter-example is k = 0 shown in the plot below.


{{{graph( 330, 330, -5.5, 5.5, -1.5, 6.5,
          2x^2+kx+3, 3 - 2x
)}}}


Plots y = {{{2x^2+3}}} (red) and y = 3 - 2x  (green)



What is the reason you post wrong problem to this forum ??


Please do not it in the future.  Thanks.