The graph of f(x) = x6 – 2x4 – 5x2 + 6 is shown below.
Asked by maham237 @ in Mathematics viewed by 612 People
The graph of f(x) = x6 – 2x4 – 5x2 + 6 is shown below.
How many roots of f(x) are rational numbers?
1
2
4
6
Answered by maham237 @
Answer:
There are two rational roots for f(x)
Step-by-step explanation:
We are given a function
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
We find that factor gives two irrational solutions as
±√3.
Hence number of rational roots are 2.
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