Q. 85.0( 2 Votes )

# The number of real values of λ for which the lines x – 2y + 3 = 0, λx + 3y + 1 = 0 and 4x – λy + 2 = 0 are concurrent isA. 0B. 1C. 2D. infinite

The given lines are

x 2y + 3 = 0 … (1)

λx + 3y + 1 = 0 … (2)

4x λy + 2 = 0 … (3)

It is given that (1), (2) and (3) are concurrent.

(6 + λ) + 2(2λ – 4) + 3(-λ2 – 12) = 0

6 + λ + 4λ – 8 – 3λ2 – 36 = 0

5λ – 3λ2 – 38 = 0

3λ2 – 5λ + 38 = 0

The discriminant of this equation is 25-4 × 3 × 38 = -431

Hence, there is no real value of λ for which the lines x 2y + 3 = 0, λx + 3y + 1 = 0 and 4x λy + 2 = 0 are concurrent.

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