Answer:
Options (C) and (F)
Step-by-step explanation:
Polynomial function is,
f(x) = x³ - x² - 5x - 3
Possible rational roots of the given function will be = [tex]\frac{\pm1, \pm3}{\pm1}[/tex]
By putting x = -1
f(-1) = (-1)³ - (-1)² -5(-1) - 3
= -1 - 1 + 5 - 3
= 0
Therefore, x = -1 will a root of the given function.
Now we apply synthetic division to get the other roots,
-1 | 1 -1 -5 -3
↓ -1 2 3
1 -2 -3 0
Therefore, factored form of the polynomial will be (x + 1)(x² - 2x - 3).
Now we will find the roots of (x² -2x - 3).
x² - 2x - 3 = x² - 3x + x - 3
= x(x - 3) + 1(x - 3)
= (x + 1)(x - 3)
For roots of the function, f(x) = 0
(x + 1)(x - 3) = 0
x = -1, 3
Therefore, roots of the function are x = -1, 3
Options (C) and (F) are the answers.
