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Q.

The interval of a for which the equation tan2 x - (a - 4) tan x + 4 - 2a = 0 has at least one solution ∀x∈[0,π/4]

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a

a∈(1,4)

b

a∈[2,3]

c

a∈(2,3)

d

a∈[1,4]

answer is B.

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Detailed Solution

tan⁡x=a−4±(a−4)2−4(4−2a)2=a−4±a2=a−2,−2

∴ tan⁡x=a−2 (∵tan⁡x≠−2)

∵     x∈0,π4∴     0≤a−2≤1⇒    2≤a≤3

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