Question

quadratic function question

Answer 1

if the functions intersect ,then x and y co-ordinates are same.
let f(x)=g(x)
so
\[2x^2+4x-1=kx-2\]
\[2x^2+(4+k)x-1+2=0\]
\[2x^2+(4+k)x+1=0\]
\[\because ~x~is~real,~so~discriminant \ge~0\]
\[(4+k)^2-4\times 2\times 1\ge 0\]
\[(4+k)^2 \ge 8\]
\[\left| 4+k \right|\ge \sqrt{8}\]
\[4+k \le -\sqrt{8}\]
\[k \le -4-\sqrt{8}\]
and
\[4+k \ge \sqrt{8}\]
\[k \ge -4+\sqrt{8}\]