Question 757768
{{{-2x^2+kx+6=0}}}


Using r and s for the zeros,


{{{r=(-k+sqrt(k^2-4(-2)6))/(-4)=(-k+sqrt(k^2+48))/(-4)}}}
{{{s=(-k-sqrt(k^2-4(-2)6))/(-4)=(-k-sqrt(k^2+48))/(-4)}}}


Better simplifying, multiplying each by {{{(-1)/(-1)}}}:
{{{r=(k-sqrt(k^2+48))/4}}}
{{{s=(k+sqrt(k^2+48))/4}}}


The product:
{{{r*s=(k-sqrt(k^2+48))(k-sqrt(k^2+48))/16=(k^2-(k^2+48))/16=-48/16=highlight(-3)}}}