Given Information:
- Sum of the zeros: 5
- Sum of the product of the zeros taken two at a time: -2
- Product of the zeros: -24

Introduction:
To find the cubic polynomial, we need to determine the coefficients of the polynomial using the given information. A cubic polynomial is of the form:
P(x) = ax^3 + bx^2 + cx + d

Step 1: Sum of the zeros
The sum of the zeros of a cubic polynomial is given by the formula:
Sum of zeros = - (coefficient of x^2) / (coefficient of x^3)

In this case, the sum of the zeros is given as 5. Therefore, we have:
5 = - b / a

Step 2: Sum of the product of the zeros taken two at a time
The sum of the product of the zeros taken two at a time is given by the formula:
Sum of product of zeros taken two at a time = (coefficient of x) / (coefficient of x^3)

In this case, the sum of the product of the zeros taken two at a time is given as -2. Therefore, we have:
-2 = c / a

Step 3: Product of the zeros
The product of the zeros of a cubic polynomial is given by the formula:
Product of zeros = (-1)^n * (constant term) / (coefficient of x^3)

In this case, the product of the zeros is given as -24. Therefore, we have:
-24 = (-1)^3 * d / a

Step 4: Finding the coefficients
Using the equations obtained from steps 1, 2, and 3, we can determine the values of the coefficients of the cubic polynomial.

From step 1: 5 = - b / a
=> b = -5a

From step 2: -2 = c / a
=> c = -2a

From step 3: -24 = (-1)^3 * d / a
=> d = -24a

Substituting these values into the cubic polynomial form, we have:
P(x) = ax^3 + (-5a)x^2 + (-2a)x + (-24a)

Simplifying the expression, we get:
P(x) = ax^3 - 5ax^2 - 2ax - 24a

Therefore, the cubic polynomial with the given zeros is:
P(x) = ax^3 - 5ax^2 - 2ax - 24a

X3 – (a + b + c) x2 + (ab + bc + ca)x – abc
Also written as :
x3 – (Sum of the zeros) x2 + (Sum of the product of the zeros taking two at a time) x – (Product of Zeros) …(1)
Given:
Sum of the zeros = 5
Sum of the product of its zeros taken two at a time -2
Product of its zeros = –24
Putting these values in the equation (1)
, we get: x3 – 5x2 – 2x + 24
Which is required polynomial