Question

(2

)
10)
Consider the roots of a cubic equation with integral coefficients:-1, and -2. The root -1 has a multiplicity of 2. Which choice is
the cubic equation?

Answer 1

To obtain the cubic equation with roots -1 and -2 (with -1 having a multiplicity of 2), we multiply the factors (x+1)(x+1)(x+2) and simplify to get the equation x^3+5x^2+8x+4.

Step-by-step explanation:

The given cubic equation has two roots, -1 and -2, with a multiplicity of 2 for -1. To find the equation, we use the fact that if a root has multiplicity 2, it appears twice in the equation.

So, the roots of the equation are -1, -1, and -2. To obtain the equation, we multiply the factors (x+1)(x+1)(x+2).

(x+1)(x+1)(x+2) = (x+1)2(x+2) = (x2+2x+1)(x+2)

Simplifying, we get the cubic equation: x3+5x2+8x+4.

Answer 2

The equation is,

`(x+1)^(2) * (x+2) = 0`

Step-by-step explanation:

According to the question, the equation is cubic and have roots -1 (with multiplicity of 2) and -2.

So, the equation is,

`(x+1)^(2) * (x+2) = 0`

[Since, when a , b , c are the roots of a cubic equation, the equation is

given by
`(x-a) * (x-b) * (x-c) = 0` ]