If the point (0,λ) is a point of the region bounded by the semicircle x=√9−y2 and the line x=0 then equation x2−2x−λ=0
A
at least one real root in [2,3]
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B
at least one real root in [−1,0]
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C
two real roots in [−1,3]
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D
no real roots in (0,2)
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Solution
The correct option is D two real roots in [−1,3] Putting (0,λ) in the given semi circle λ=±3 Now corresponding to λ=−3 there is no real roots of the given quadratic. And corresponding to λ=3 roots are −1,3