If the line `y=3x+lambda` intersects the parabola `y^2=4x` at two distinct points then set of values of `lambda`

Explanation

Putting value of y from the line in the parabola
`-(3x+lamda)^(2)=4x`
`!9x^(2)+(6lamda-4)x+lamda^(2)=0`
`because` line cuts the parabola at two distinct points
`thereforeDgt0`
`!4(3lamda-2)^(2)-4.9lamda^(2)gt0`
`!9lamda^(2)-12lamda+4-9lamda^(2)gt0`
`!lamdalt1//3` Hence, `lamdain(-oo,1//3)`