The straight line y=2x+λ does not meet the parabola y2=2x, if
λ>14
Line− y=2x+λ .......(i)Parabola− y2=2x ......(ii)Solving (i) & (ii) we get, (2x+λ)2=2x⇒4x2+4xλ+λ2=2x⇒4x2+2x(2λ−1)+λ2=0
Line does not meet the parabola
⇒D<0⇒4(2λ−1)2−4(4)(λ2)<0⇒4[4λ2+1−4λ−4λ2]<0⇒1−4λ<0⇒λ>14