Question

Find the roots of the equation $x^2-2xcos\theta$ + 1 = 0.

• A. ,
• B. ,
• C. ,
• D. ,

Answer 1

The correct option is A

,

Solution: Given equation $x^2-2xcos\theta$ + 1 = 0.

Roots of quadratic equation using quadratic formulae

x = $\frac{-b\underset{–}{+}\sqrt{b^2-4ac}}{2a}$

x = $\frac{2cos\theta \underset{–}{+}\sqrt{4co{s}^2\theta -4}}{2}$

= $cos\theta \underset{–}{+}\sqrt{co{s}^2\theta -1}$

= $cos\theta \underset{–}{+}isin\theta$

= $e^{i\theta }$ and $e^{-i\theta }$.