Question

• Given the function, f(x) = x3 – 5x2 + 9x – 45, determine the number of roots and identify them.

Answer 1

x3 - 5x2 + 9x - 45 = 0
 It is a polynomial of degree three, therefore, it has three roots.
 For this case, what we can do is factorize to write the polynomial in an easier way and thus be able to find the roots.
 Factoring we have:
 (x - 5) (x ^ 2 + 9) = 0
 x = 5
 x = 3i
 x = -3i
 Answer: 
 three roots: 
 x = 5 
 x = 3i 
 x = -3i