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,

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.