Answer:
The roots of the of the function are 2,3 and 4.
Step-by-step explanation:
The given function is
f(x) = x³ - 9x² + 26x - 24
It is given that x=2 is a root of the function. So (x-2) is a factor of f(x).
According to the remainder theorem if a function is divided by (x-c), then the remainder is equal to f(c). If f(c) is equal to 0, therefore c is the root of the function.
Use synthetic method to divide f(x) by (x-2).
f(x) = (x - 2) (x² - 7x + 12)
<em>f(x)= (x - 2) (x² - 4x - 3x + 12)</em>
<em>f(x)= (x - 2) (x(x - 4) - 3(x - 4))</em>
f(x)= (x - 2) (x - 4) (x - 3)
To find the roots equation the function equate the function equal to 0.
0 = (x - 2) (x - 4) (x - 3)
Equate each factor equal to 0.
x = 2,3,4
Therefore the roots of the function are 2,3 and 4.
(btw this is someone else's answer i found since i got a little confused myself heh)
