Question

The roots of the equation $x^4-2x^3+x=380$ are :

• A. $5,-4,\frac{1\pm 5\sqrt{-3}}{2}$
• B. $-5,4,\frac{-1\pm 5\sqrt{-3}}{2}$
• C. $5,4,\frac{-1\pm 5\sqrt{-3}}{2}$
• D. $-5,-4,\frac{1\pm 5\sqrt{-3}}{2}$

Answer 1

Answer: (A)

Given equation is $x^4-2x^3+x-380=0$
$\Rightarrow \left(x^2-x-20\right)\left(x^2-x+19\right)=0$
$\Rightarrow (x-5)(x+4)\left(x^2-x+19\right)=0$
Hence, the required roots of the equation are
$5,-4,\frac{1\pm 5\sqrt{-3}}{2}$