Question

Conjecture: How many solutions do x3 - 5x2 + 28 = 0 have? Find the real solution(s) of the equation. Then use polynomial long division to find the other solution(s).

Answer 1

x = - 2 is confirmed to be the real solution of the equation.

Explanation:

We are tasked with the following activities

Conjecture: How many solutions do
`x^3 - 5x^2 + 28 = 0` have?

Find the real solution(s) of the equation.

Then use polynomial long division to find the other solution(s).

To start with the how many solutions that
`x^3 - 5x^2 + 28 = 0` have

suppose that -2 happens to be a root of the equation, we can easily replace x = - 2 in the given equation. Then , we will have :

`(-2)^3 - 5(-2)^2 + 28 = 0`

`-8 - 5* 4 + 28 = 0`

-8 - 20 + 28 = 0

-28 - 28 = 0

0 = 0

The equation resulted to 0 = 0 when x = -2 , as such -2 happens to be one root of the equation

So , as x = - 2

x + 2 = 0

x = - 2 is confirmed to be the real solution of the equation.

A picture showing the polynomial long division method used for solving the polynomial equation and other solution(s) can be found in the attached file below.