What are the real and complex solutions of the polynomial equation? x^4-41x^2=-400. *work needed*

Step-by-step explanation:

Given the polynomial equation .

Adding 400 on both sides to get rid 400 from right side and set 0 on right side, we get

.

.

Factoring by product sum rule.

We need product of 400 and sum upto -41.

We can see that 400 = -25 × -16 = 400 and -25-16 = -41.

Therefore,

Making it into two groups, we get

Factoring out GCF of each group, we get

Factoring out   and separately by difference of the squares identity , we get

and

.

Therefore,

Applying zero product rule,

x-5=0

x+5=0

x-4=0 and

x+4=0.

Therefore,