Question

The roots of the equation $4x^4-24x^3+57x^2+18x-45=0$ if one of them is $3+i\sqrt{6}$ , are

• A. $3-i\sqrt{6},\pm \frac{\sqrt{3}}{2}$
• B. $-\sqrt{\frac{3}{2}}$
• C. $3-i\sqrt{6},\pm \frac{3}{\sqrt{2}}$
• D. None of these

Answer 1

The correct option is A

$3-i\sqrt{6},\pm \frac{\sqrt{3}}{2}$

$x^2$ – 6x + 15 = 0 is quadratic corresponding to roots $3\pm i\sqrt{6}$ and dividing the given equation by this, we get $4x^2-3=0\Rightarrow x=\pm \frac{\sqrt{3}}{2}$