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Answer:
x = 5, x = -i√7, x = i√7
Step-by-step explanation:
We can factor the equation x³ - 5x² + 7x - 35 = 0 by grouping:
x²(x - 5) + 7(x -5) = 0
We get:
(x² + 7)(x - 5) = 0
or
(x + i√7)(x - i√7)(x - 5) = 0
Use the Zero Product Property to solve for the solutions:
x - 5 = 0
x = 5.
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x² + 7 = 0
x² = -7 (We will have imaginary solutions in this instance)
x = ±i√7
Therefore, the zeros of this equation are:
x = 5, x = -i√7, x = i√7
