form a cubic polynomial of zeroes 3,2and-1
Answers
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:
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.