How do you solve 2x4−128=0?
1 Answer
Jan 10, 2017
The roots of this quartic equation are:
±2√2 and±2√2i
Explanation:
The difference of squares identity can be written:
a2−b2=(a−b)(a+b)
So we find:
0=2x4−128
0=2(x4−64)
0=2((x2)2−82)
0=2(x2−8)(x2+8)
0=2(x2−(2√2)2)(x2−(2√2i)2)
0=2(x−2√2)(x+2√2)(x−2√2i)(x+2√2i)
So the roots of the quartic equation are:
±2√2 and±2√2i