Find all the zeroes of the polynomial x3 - 6x2 +11x - 6 if two of its

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

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

Answer»

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.

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

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