Which of the following represents the zeros of f(x) = x³ - 12x² + 41x - 42?

Solution:

It is given that

Function f(x) = x³ - 12x² + 41x - 42

Using the synthetic division we get,

So we get

(x - 2)(x² - 10x + 21) = 0

Splitting the middle term

(x - 2)(x² - 3x - 7x + 21) = 0

(x - 2)[x(x - 3) - 7(x - 3)] = 0

We get,

(x - 2)(x - 3)(x - 7) = 0

Here

x = 2, x = 3, and x = 7

Therefore, 2, 3 and 7 represent the zeros of f(x) = x³ - 12x² + 41x - 42.

---

Which of the following represents the zeros of f(x) = x³ - 12x² + 41x - 42?

Summary:

2, 3 and 7 represent the zeros of f(x) = x³ - 12x² + 41x - 42.