<h3>
Answer: x = -5, -4, 4 and 5.</h3><h3>All four zeros are real solutions.</h3>
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,
![x^4-25x^2-16x^2+400=0](https://tex.z-dn.net/?f=x%5E4-25x%5E2-16x%5E2%2B400%3D0)
Making it into two groups, we get
![(x^4-25x^2)+(-16x^2+400)=0](https://tex.z-dn.net/?f=%28x%5E4-25x%5E2%29%2B%28-16x%5E2%2B400%29%3D0)
Factoring out GCF of each group, we get
![x^2(x^2-25)-16(x^2-25)=0](https://tex.z-dn.net/?f=x%5E2%28x%5E2-25%29-16%28x%5E2-25%29%3D0)
![(x^2-25)(x^2-16) =0](https://tex.z-dn.net/?f=%28x%5E2-25%29%28x%5E2-16%29%20%3D0)
Factoring out
and
separately by difference of the squares identity
, we get
and
.
Therefore,
![(x-5)(x+5)(x-4)(x+4) =0](https://tex.z-dn.net/?f=%28x-5%29%28x%2B5%29%28x-4%29%28x%2B4%29%20%3D0)
Applying zero product rule,
x-5=0
x+5=0
x-4=0 and
x+4=0.
Therefore,
<h3>x = -5, -4, 4 and 5.</h3><h3>All four zeros are real solutions.</h3>