Question

If one zero of the polynomial p(x)=x³-6x²+11x-6 is 3.Find the other two zeroes.[Don't spam]

Answer 1

p(x) = x³ - 6x² + 11x -6

One zero is 3

Means one factor is x = 3

x -3 =0

One factor is (x - 3).

Now , divide x³ - 6x² + 11x -6 by ( x-3 ). So,

x - 3) x³ - 6x² + 11x -6 ( x² - 3x + 2

x³ - 3x²

(-) (+)

______________

3x² + 11x -6

3x² + 9x

(-) (+)

_______________

2x - 6

2x - 6

(-) (+)

____________

0

___________

❅ x² - 3x + 2

➟ x² - ( 2+ 1) x + 2

➟ x² -2x - x + 2

➟ x (x -1) - 2(x-1)

➟ (x-1) (x-2)

Other two zeros of this polynomial are:-

➙ x - 1 =0

➙ x = 1

➙ x - 2=0

➙ x = 2

❝ Hence, other two zeros are 1 and 2.❞

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Answer 2

Hence, the other two zeroes are 1 & 2.

Regards!