Question

Determine how many, what type, and find the roots for f(x) = x3 − 5x2 − 25x + 125.

Answer 1

hello :
by grouping method :
f(x) = x3 − 5x2 − 25x + 125. = x²(x - 5) - 25(x - 5)
f(x) =(x -5)( x² -25)= ( x -5) ( x -5)(x +5)
f(x) = (x-5)²(x+5)

Answer 2

Explanation:

Given that the function

f(x) = x^3-5x^2-25x+125

We have to find the roots of f(x)

Let us try to factorize the function to find the roots

We can group two by two and find out

f(x) = x^2(x-5)-25(x-5)\\

=(x^2-25)(x-5)

=(x+5)(x-5)^2

We find that the roots are -5,5,5

Or -5 with a multiplicity of 1

and 5 with a multiplicity of 2 are the roots of the equation