Approximate the real number solution(s) to the polynomial function f(x) = x³ - 2x² - 5x + 6.

Solution:

Given, the polynomial function f(x) = x³ - 2x² - 5x + 6.

From the above function, the sum of the coefficients (1 - 2 - 5 + 6) is 0.

Since, the sum of coefficients is zero, (x - 1) is a factor of the function.

By using long division,

The quotient is x² - x - 6

On solving,

x² - x - 6 = 0

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

So, x = 3 or -2.

Therefore, the real number solutions are x = 1, 3 and -2.

Approximate the real number solution(s) to the polynomial function f(x) = x³ - 2x² - 5x + 6.

Summary:

The real number solution(s) to the polynomial function f(x) = x³ - 2x² - 5x + 6 are x = 1, 3 and -2.