Question

form a cubic polynomial of zeroes 3,2and-1​

Answer 1

Explanation:

x³ - 4x² + x + 6

Step-by-step explanation:

Let the zeroes be α,β,γ.

Given Zeroes are 3,2,-1.

(i) Sum of its Zeroes:

⇒ α + β + γ = 3 + 2 - 1

                   = 4.

(ii) Sum of the product taken two at a time:

⇒ αβ + βγ + γα = 3 * 2 + 2 * -1 + 3 * -1

                         = 1

(iii) Product of its zeroes:

⇒ αβγ = 3 * 2 * -1

           = -6.

Therefore, the cubic polynomial can be:

= x³ - (Sum of its zeroes)x² + (Sum of product taken two at a time)x - (Product of its zero)

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

= x³ - 4x² + x + 6.

Therefore, the cubic polynomial is x³ - 4x² + x + 6.

hope it will help you

Answer 2

Answer:

x³ - 4x² + x + 6

Explanation:

Let the zeroes be α,β,γ.

Given Zeroes are 3,2,-1.

(i) Sum of its Zeroes:

⇒ α + β + γ = 3 + 2 - 1

                  = 4.

(ii) Sum of the product taken two at a time:

⇒ αβ + βγ + γα = 3 * 2 + 2 * -1 + 3 * -1

                        = 1

(iii) Product of its zeroes:

⇒ αβγ = 3 * 2 * -1

          = -6.

Therefore, the cubic polynomial can be:

= x³ - (Sum of its zeroes)x² + (Sum of product taken two at a time)x - (Product of its zero)

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

= x³ - 4x² + x + 6.

Therefore, the cubic polynomial is x³ - 4x² + x + 6.