Respuesta :
Answer:
There are two rational roots for f(x)
Step-by-step explanation:
We are given a function
[tex]f(x) = x^6-2x^4-5x^2+6[/tex]
To find the number of rational roots for f(x).
Let us use remainder theorem that when
f(a) =0, (x-a) is a factor of f(x) or x=a is one solution.
Substitute 1 for x
f(1) = 1-2-5+6=0
Hence x=1 is one solution.
Let us try x=-1
f(-1) = 1-2-5+6 =0
So x =-1 is also a solution and x+1 is a factor
We can write f(x) by trial and error as
[tex]f(x) = (x-1)(x+1)(x^2-3)[/tex]
We find that [tex]f(x) (x^2-3)[/tex] factor gives two irrational solutions as
±√3.
Hence number of rational roots are 2.
