How to form a cubic polynomial when zeros are given

Asked by admin @ in Math viewed by 253 People

Form a cubic polynomial whose zeros are 3 ,2 and -1 hence

(i) find sum of its zero (ii) sum of the product taken two at a time(iii)product of its zero BETTER ANS WILL BE MARKED AS BRAINLIEST ✌️

Answered by admin @


Answer:

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 helps!






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