Question

Find the cubic polynomial whose zeros are - 2 - 3 and -1

Answer 1

Answer:

x³ + 6x² + 11x + 6

Step-by-step explanation:

Let the zeroes of the cubic polynomial be α, β and γ respectively. Thus,

• α = (-2)
• β = (-3)
• γ = (-1)

Sum of roots = α + β + γ

⇒ (-2) + (-3) + (-1)

⇒ - 2 - 3 - 1

⇒ - 6

Sum of products of roots = αβ + βγ + γα

⇒ (-2)(-3) + (-3)(-1) + (-1)(-2)

⇒ 6 + 3 + 2

⇒ 11

Product of roots = αβγ

⇒ (-2) * (-3) * (-1)

⇒ 6 * (-1)

⇒ - 6

Now, cubic polynomial is given by -

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

= x³ - (-6)x² + 11x - (-6)

= x³ + 6x² + 11x + 6

Hence, the required cubic polynomial is x³ + 6x² + 11x + 6.

Answer 2

Answer:

answer : x³ + 6x² +11x +6

answer