Question

find a cubic polynomial whose zeros are 3,4,and -2​

Answer 1

Step-by-step explanation:

Given :-

Zeroes are 3 , 4 and -2

To find :-

Find the Cubic Polynomial with the zeores ?

Solution :-

Given zeores are 3,4 and -2

Let α = 3

Let β = 4

Let γ = -2

Sum of the zeores = α+β+γ

=> α+β+γ = 3+4+(-2)

=> α+β+γ = 3+4-2

=> α+β+γ = 7-2

α+β+γ = 5 ------------(1)

Sum of the product of the two zeroes taken at a time = αβ+βγ +αγ

=> αβ+βγ +αγ = (3)(4)+(4)(-2)+(-2)(3)

=> αβ+βγ +αγ = 12+(-8)+(-6)

=> αβ+βγ +αγ = 12-8-6

=> αβ+βγ +αγ = 12-14

=> αβ+βγ +αγ = -2 ----------(2)

and

Product of the zeroes = αβγ

=>αβγ = (3)(4)(-2)

=>αβγ = -24 ---------(3)

We know that

The Cubic Polynomial whose zeroes are α,β,γ is

K[x³-(α+β+γ )x²+(αβ+βγ +αγ)x-αβγ]

From (1),(2) and (3)

=> K[x³-(5)x²+(-2)x-(-24)]

=> K[x³-5x²-2x+24]

If K = 1 then the required Polynomial is x³-5x²-2x+24

Answer:-

The required Cubic Polynomial is x³-5x²-2x+24

Used formulae:-

• The standard cubic polynomial is ax³+bx²+cx+d

• The Cubic Polynomial whose zeroes are α,β,γ is K[x³-(α+β+γ )x²+(αβ+βγ +αγ)x-αβγ]

Answer 2

sorry for spamming..I hope that mods will delete this answer report krdo please.report it