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

Answer: the real solution: x = - 2

Find the attached file for the remaining solution

Explanation:

The equation given is:

x3 - 5x2 + 28 = 0

Let assume that -2 is one of the root of the equation. Substitute -2 for x

(-2)^3 - 5(-2)^2 + 28

-8 - 20 + 28 = 0

Therefore, -2 is one of the root of the equation since the equation tend to zero.

If x = -2, then x+2 is one of the factors of the equation. Therefore, the real solution is x = -2

Please find the attached file for the remaining solution.