A) \[\theta \] is an acute angle
B) \[\theta \] is a right angle
C) \[\theta \]is an obtuse angle
D) No value of \[\theta \]is possible
Correct Answer: D
Solution :
The quadratic equation is \[{{x}^{2}}-x\cos \theta +1=0\] But x is real, therefore \[{{B}^{2}}-4AC\ge 0\] \[\Rightarrow {{\cos }^{2}}\theta \ge 4(1)(1)\Rightarrow {{\cos }^{2}}\theta \ge 4\], which is impossible.
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