College

Find all the zeros of the equation:

\[ x^5 - 3x^4 - 15x^3 + 45x^2 - 16x + 48 = 0 \]

A. 3, 4, i
B. 4, -4, i-i
C. 3, 4, 4, i, -i
D. 3, -4, -i

Answer :

Final answer:

To find the zeros of the equation, factor the polynomial and solve for x. The zeros are 3, 4, -4, i, and -i.


Explanation:

To find the zeros of the equation x5 - 3x4 - 15x3 + 45x2 - 16x + 48 = 0, we need to factor the polynomial and solve for x. By factoring, we can rewrite the equation as (x - 3)(x - 4)(x + 4)(x - i)(x + i) = 0. Therefore, the zeros are x = 3, x = 4, x = -4, x = i, and x = -i.


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