Question

If 2x + y = 0 is one of the lines represented by 3x² + kxy + 2y² = 0, then the value of k is

Options

• `1/2`

• `11/2`

• `5/2`

• `(-11)/2`

Answer 1

Auxiliary equation of the given equation is 2m² + km + 3 = 0.

Slope of the line 2x + y = 0 is m = − 2.

∴ m = −2 is a root of the auxiliary equation 2m² + km + 3 = 0

∴ 2(−2)² − 2k + 3 = 0

∴ 8 − 2k + 3 = 0

∴ k = `11/2`