Question

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

Answer 1

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.