(1/2)

Sol. Period of y = 2sin x is = & y = α (x – 1)(x – 2) + 1 which is a quadratic. So for given information (1, 1) is the common point to two curves and the possible graph would the

α can not be nagative α must be positive

for these twp graphs to touch each other at (1, 1)

(Which can be the only possible point of contact) of both curves must be same.

y = 2sin x ⇒ = .

= = .cos = – ...(1)

y = α x 2 – 3 α x + 2 α + 1 ⇒ = 2 α x – 3 α

= 2 α –3 α = – α ....(2)

for (1) & (2) α = ⇒ =

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