Find all the zeros of the function and write the polynomial as a product of linear factors. X⁴ - 81 A)3,3i; (x + 3)(x + 3)(x - 3i)(x - 3i) B)±3i; (x - 3i)(x + 3i) C)±3,±3i; (x - 3)(x - 3)(x + 3i)(x + 3i) D)±3; (x - 3)(x + 3) E)±3,±3i; (x - 3)(x + 3)(x - 3i)(x + 3i)

Question

Quizplus · Accepted Answer

The given polynomial can be written as:
X^4 + 14X^2 -81 = (X^2 + 9)(X^2 - 9) = (X^2 + 9)(X + 3)(X - 3)
Further, we can write:
(X^2 + 9) = (X + 3i)(X - 3i)
Hence, the zeros of the polynomial are ±3, ±3i and it can be written as a product of linear factors as (x - 3)(x + 3)(x - 3i)(x + 3i), which is best represented by choice letter E.

Find All the Zeros of the Function and Write the Polynomial