Solve x^4 + x^2 – 2 = 0. (Multiple Choice)

Question

a. x = ±1 or x = ±i
b. x = ±1 or x = i√2
c. x = ±1 or x = ±2
d. x = ±1 or x = √2

Answer 1

x⁴+x²-2=0

 

Let y = x²

 

y² + y - 2 = 0

 

(y+2)(y-1) = 0

 

but y = x² so this factors to

 

(x²+2)(x²-1) = 0

 

Either x² + 2 = 0         or   x²-1 = 0

         x² = -2                    x²=1

         x = ± √(-2)              x = ±√1

            x = ±i√2                  x = ± 1

 

The actual correct answer is not there.   x = ±1 or x = ±i√2

 

Assuming it was an honest mistake, if there is such a thing, the closest "correct answer" is b

 

 

Answer 2

b is the answer.

 

When you factor you get:

 

(x^2 -1)(x^2 +2) = 0

 

The first factor will give you x = +/-1, and the second will give you i times radical 2