Question

The number of values of k for which the linear equations 4x + ky + 2z = 0, kx + 4y + z = 0 and 2x + 2y + z = 0 possess a non-zero solution is

विकल्प

• 2

• 1

• zero

• 3

Answer 1

2

Explanation:

Δ = 0 ⇒ `|(4, k, 2),(k, 4, 1),(2, 2, 1)|` = 0

⇒ `4(4 - 2) - k(k - 2) + 2(2k - 8)` = 0

⇒ `8 - k^2 + 2k + 4k - 16` = 0

⇒ `k^2 - 6k + 8` = 0

⇒ `(k - 4)(k - 2)` = 0

⇒ `k` = 4, 2