Question

Find a cubic palynomial whose zeroes are -2 -3 and -1 ​

Answer 1

Answer:

x^3+6x^2+11x+6

Step-by-step explanation:

zeroes are -2,-3,-1

then it's factors will be

(X+2)(X+3)(X+1)

(x^2+3x+2x+6)(X+1)

(x^2+5x+6)(X+1)

x^3+x^2+5x^2+5x+6x+6

x^3+6x^2+11x+6

Answer 2

Given :-

• Zeroes of a polynomial are -2, -3, -1

To Find :-

• The cubic polynomial

Solution :-

Let α, β and γ be the zeroes of the given polynomial.

Therefore,

α = -2

β = -3

γ = -1

Formula to be used :-

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

At first, find the sum and product of the zeroes

⟹ (α + β + γ ) = -2 + (-3) + (-1)

⟹ (α + β + γ) = -2 - 3 - 1

⟹(α + β + γ) = -6

_____

⟹αβγ = -2 × -3 × -1

⟹αβγ = -6

_________________________________________

Again, find the value of (αβ + βγ + γα)

⟹ (αβ + βγ + γα)

= -2 × (-3) + (-3) × (-1) + (-1) ×(-2)

= 6 + 3 + 2

= 11

According to the question, we are asked to find a polynomial whose zeroes are -2, -3 and -1 .

Now, find the polynomial ____

General structure of a polynomial __

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

Put the values of (α + β +γ ), (αβ + βγ + γα) and (αβγ) in the formula .

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

⟼ x³ -(-6)x² + (11)x - (-6)

⟼ x³ + 6x² + 11x + 6

$The \: \: cubic \: \: polynomial \: \: is = x³ + 6x² + 11x +6$