Q12 of 90 Page 2

Find a cubic polynomial having 1, 2, 3 as its zeroes.

Let the zeroes of the cubic polynomial be


α = 1, β = 2 and γ = 3


Then, α + β + γ = 1 + 2 + 3 = 6


αβ + βγ + γα = (1)(2) + (2)(3) + (3)(1)


= 2 + 6 + 3


= 11


and αβγ = 1 × 2 × 3


= 6


Now, required cubic polynomial


= x3 – (α + β + γ) x2 + (αβ + βγ + γα)x – αβγ


= x3 – (6) x2 + (11)x – 6


= x3 – 6 x2 + 11x – 6


So, x3 – 6 x2 + 11x – 6 is the required cubic polynomial which satisfy the given conditions.


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