Question

If $o<\alpha <\beta <\gamma <\frac{\pi }{2}$, then the equation $\frac{1}{x-\sin \alpha }+\frac{1}{x-\sin \beta }+\frac{1}{x-\sin \gamma }=0$ has

• A. Imaginary roots
• B. Real and equal roots
• C. Real and unequal roots
• D. Rational roots

Answer 1

The correct option is A Imaginary roots

$\begin{array}{c}\frac{1}{x-\sin \alpha }+\frac{1}{x-\sin \beta }+\frac{1}{x-\sin \gamma }=0\\ 0<\alpha <\beta <\gamma <\frac{\pi }{2}\\ let\alpha ={30}^0,\beta ={45}^0,\gamma ={60}^0\\ \Rightarrow \frac{1}{x-\frac{1}{2}}=\frac{1}{x-2\sqrt{2}}=\frac{1}{x-\sqrt{\frac{3}{2}}}=0\end{array}$

hence roots are real and unequal