Complex Numbers And Quadratic Equations question 799
Question: If $ \sin A,\sin B,\cos A $ are in G.P., then roots of $ x^{2}+2x\cot B+1=0 $ are always [Orissa JEE 2005]
Options:
A) Real
B) Imaginary
C) Greater than 1
D) Equal
Show Answer
Answer:
Correct Answer: A
Solution:
Given $ {{\sin }^{2}}B=\sin A\cos A $
Þ $ \cos 2B=1-\sin 2A\ge 0 $ Now for $ x^{2}+2x\cot B+1=0 $ Consider $ D=4({{\cot }^{2}}B-1)=4\cos 2B\cos e{c^{2}}B\ge 0 $ Hence, roots are always real.
BETA
