Q. 84.9( 10 Votes )

Find a cubic polynomial whose zeroes are 0, 1, 2.

Answer :

A cubic polynomial having α, β, and γ as zeroes is given by,

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

Explanation:

α + β + γ = 0 + 1 + 2 = 3

αβ + βγ + γα = 0 × 1 + 1 × 2 + 2 × 0

αβ + βγ + γα = 0 + 2 + 0 = 2

αβγ = 0 × 1 × 2 = 0

Putting the values, we get,

P(x) = x3 – (3)x2 + (2)x – (0)

P(x) = x3 – 3x2 + 2x 

Therefore, P(x) = x3 – 3x2 + 2x 

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