Question

The graph of f(x) = x6 – 2x4 – 5x2 + 6 is shown below.

Answer 1

Answer:

There are two rational roots for f(x)

Step-by-step explanation:

We are given a function

$f(x) = x^6-2x^4-5x^2+6$

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

$f(x) = (x-1)(x+1)(x^2-3)$

We find that $f(x) (x^2-3)$ factor gives two irrational solutions as

±√3.

Hence number of rational roots are 2.

Answer 2

Answer:

B. 2

Step-by-step explanation:

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