Question

Which of the following are solutions to the equation X^4-2x³ + x = 2?

1. X=-1
II. X=2
1±i√3
III. X= 2
IV. X=2±3/i

Answer 1

x=2, x=−1

Explanation:

x^4−2x^3+x=2

Subtract 2 from both sides

x^4−2x^3+x−2=2−2

Simplify

x^4−2x^3+x−2=0

Factor x^4−2x^3+x−2:

=(x−2)(x+1)(x2−x+1)

x−2=0 or x+1=0​

Thus

x=2, x=-1