Question

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 ✌️

Answer 1

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!

Answer 2

Let the cubic polynomial be p(x)

It's zeros are 3,2,-1

So the factors will be (x-3),(x-2),(x+1)

A cubic polynomial will at most have three zeros

So by multiplying all its three factors, we will get the polynomial

(x-3)(x-2)(x+1)

=(x²-2x-3x+6)(x+1)

=(x²-5x+6)(x+1)

=x³+x²-5x²-5x+6x+6

=x³-4x²+x+6