Q17 of 113 Page 71

If one zero of the polynomial p(x) = x3 – 6x2 + 11x – 6 is 3, find the other two zeros.

It is given in the question that,

p (x) = x3 – 6x2 + 11x – 6 having factor (x + 3)


Now, we have to divide p (x) by (x – 3)


x3 – 6x2 + 11x – 6 = (x – 3) (x3 – 3x + 2)


= (x – 3) [(x2 – (2 + 1) x + 2]


= (x – 3) (x2 – 2x – x + 2)


= (x – 3) [x (x – 2) – 1 (x – 2)]


= (x – 3) (x - 1) (x – 2)


Hence, the two zeros of the polynomial are 1 and 2


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