Q.
Let α, β, γ be distinct real numbers lying in (0, π/2), then the equation 1x−sinα+1x−sinβ+1x−sinγ=0, has
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a
two distinct real roots
b
two equal roots
c
two imaginary roots
d
one real and one imaginary root.
answer is A.
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Detailed Solution
Let a=sinα, b=sinβ, c=sinγNote that a,b,c are distinct and 00 f(b)=(b-c)(b-a)<0and f(c)=(c-a)(c-b)>0.Thus, f(x)=0 has a root in (a,b) and a root in (b,c).
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