Question

Find the cubic polynomial whose roots are -2, -3 and -5.

Answer 1

The cubic polynomial is
(x+2)(x+3)(x+5)
= (x^2+5x+6)(x+5)
= x^3+10x^2+11x+30

Answer 2

Hey dear!!

___________________________

==> In the example,

-2 , -3 and -5 are the roots given .

We have to find the cubic polynomial which satisfies this given roots (zeroes).

==> Solution:

Let, α = -2 , β = -3 and γ = -5

We know that,

Sum of zeroes = α + β + γ

∴ α + β + γ = -2 + (-3) + (-5)

= -2 -3 - 5

= -5 - 5

= -10

∴ α + β + γ = [ -10 ]

We also know,

Product of zeroes => αβ + βγ + γα

∴ αβ + βγ + γα = -2(-3) + (-3)(-5) + (-5)(-2)

= 6 + 15 +10

= 21 + 10

= 31

∴ αβ + βγ +γα = 31

Aslo,

αβγ = -2(-3)(-5)

= 6(-5)

= -30

∴ αβγ = -30

Now, the required cubic polynomial .

We Know that,

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

x³ - (-10)x² + 31x - (-30)

x³ + 10x² + 31x + 30

Therefore , the required cubic polynomial is [ x³ + 10x² +31x + 30 ]

Thanks !!!

[ Be Brainly ]