Question

Find all the zeroes of the polynomial x³ - 6x² +11x - 6 if two of its zeroes are 1 and 2.

Answer 1

Let f(x) = x³ - 6x² + 11x - 6 

Given: (x-1)(x-2) are the zeros of f(x). 

product of zeros = (x-1)(x-2) = x² - 2x - x + 2 = x² -3x + 2 

therefore, on dividing the f(x) with x² - 3x + 2 , we get, x-3 

Now, x - 3 = 0 

x = 3

Hence, the other zero is 3.