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 r = $\sqrt{2}$
• D. Rectangle in a circle of r = $\sqrt{2}$

Answer 1

Answer: (D)

Rectangle in a circle of r = $\sqrt{2}$

Answer 2

The roots are $\sqrt { 2 }$ $e^{i\frac{\pi}{6}}$, – $\sqrt { 2 }$ $e^{i\pi/6}$, $\sqrt { 2 }$ $e^{- i\frac{\pi}{6}}$, –$\sqrt { 2 }$ $e^{- i\frac{\pi}{6}}$. They lie on a circle of radius $\sqrt{2}$ units as diagonals intersect at an angle$\frac{\pi}{3}$, then are vertices of an inscribed rectangle.