If the equation `2x^(2)+kxy+2y^(2)=0` represents a pair of real and distinct lines , then find the values of k.

Options

A. `lambda in (-4, 4)`
B. `lambda in R`
C. `lambda in (-oo,-4)uu(4,oo)`
D. `lambda = 4, -4`

Answer

C

Explanation

The equation `2x^(2)+lambdaxy+2y^(2)=0` will represent a pair of real and distinct lines, if
`((lambda)/(2))^(2)-2xx2gt0" "["Using : h"^(2) gt ab]`
`rArr" "lambda^(2)-16gt0 rArr lambda in (-oo,-4)uu(4,oo)`