Question

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

• A. $5, - 4 , \frac{1\pm5\sqrt{-3}}{2}$
• B. $- 5, 4 , \frac{- 1\pm5\sqrt{-3}}{2}$
• C. $5, 4 , \frac{-1\pm5\sqrt{-3}}{2}$
• D. $-5, - 4 , \frac{1\pm5\sqrt{-3}}{2}$

Answer 1

Answer: (A)

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