Question

Find ALL zeros
x^4 + 10x^2 +9 =0

Answer 1

The zeros are x = ±i or x = ±3i.

Step-by-step explanation:

To find all the zeros of the equation x4 + 10x2 + 9 = 0, we can use factoring.

Firstly, let's substitute x2 as y, then the equation becomes y2 + 10y + 9 = 0.

Now we can factor this quadratic equation as (y + 1)(y + 9) = 0.

Setting each factor equal to zero, we get y + 1 = 0 or y + 9 = 0.

Solving these equations, we have y = -1 or y = -9.

Finally, substituting x2 back into y, we get x = ±√(-1) or x = ±√(-9), which simplifies to x = ±i or x = ±3i.