Question

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

Answer 1

Let the zeroes of the cubic polynomial be

α = – 3, β = – 2 and γ = 2

Then, α + β + γ = – 3 + ( – 2) + 2

= – 3 – 2 + 2

= – 3

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

= 6 – 4 – 6

= – 4

and αβγ = ( – 3) × ( – 2) × 2

= 6 × 2

= 12

Now, required cubic polynomial

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

= x³ – ( – 3) x² + ( – 4)x – 12

= x³ + 3 x² – 4x – 12

So, x³ + 3x² – 4x – 12 is the required cubic polynomial which satisfy the given conditions.