Question

The roots of the equation x⁴ – 2x² + 4 = 0 are the vertices of a

• A. Square inscribed in a circle of radius 2
• B. Rectangle inscribed in a circle of radius 2
• C. Square inscribed in a circle of radius$\sqrt{2}$.
• D. Rectangle inscribed in a circle of radius.

Answer 1

Answer: (D)

Rectangle inscribed in a circle of radius.

Answer 2

Sol. Here, the roots of the equation x⁴ – 2x² + 4 = 0 are :

$\sqrt{2}e^{i\pi/6}$, – $\sqrt{2}e^{i\pi/6}$, $\sqrt{2}e^{–i\pi/6}$, – $\sqrt{2}e^{–i\pi/6}$

These points lies on a circle of radius $\sqrt{2}$, as the diagonals intersect at an angle $\frac{\pi}{3}$,

\ These are the vertices of an inscribed rectangle.