Question

Given the function, where a, b, and c are positive numbers:
f(x) = (x - a)(x - b)2(x2 + c)
How many real roots does f(x) have, including multiple roots? |
How many imaginary roots does f(x) have?

Answer 1

Answer:

2 real roots and 1 imaginary roots

Step-by-step explanation:

f(x) = $(x-a)(x-b)^{2} (x^{2}+c)$

There are only 2 real roots and one imaginary roots.

Separate the equation into sections because the function is a multiplication with no outside sum or substraction:

Real Roots:

$(x-a)$ = 0 when x = a

$(x-b)^{2}$ = 0 when x = b

Imaginary roots:

$(x^{2}-c)$ = 0 when x = $\sqrt{-c}$