Question

HELP!!!!!!!!!!!

The graph of f(x) = 4x3 – 13x2 + 9x + 2 is shown below.
How many roots of f(x) are rational numbers?
A.) 0
B.) 1
C.) 2
D.) 3

Answer 1

B on edgeentrash

Explanation:

Answer 2

One rational root.

B is correct.

Explanation:

Given: The graph of
`f(x)=4x^3-13x^2+9x+2`

First we factor the given function.

Factor of f(x)

f(2)=0 , x-2 must be factor of f(x)

`f(x)=(x-2)(4x^2-5x-1)`

Because f(2)=0

So, x=2 is rational root of f(x)

Now we find another root using quadratic formula.

`ax^2+bx+c=0`

`\text{Quadratic formula: }x=(-b\pm√(b^2-4ac))/(2a)`

where, a=4, b=-5 and c=-1

`x=(-(-5)\pm √((-5)^2-4(4)(-1)))/(2(4))`

`x=(5\pm√(41))/(8)`

Another roots are,

`x=(5+√(41))/(8),(5-√(41))/(8)`

So, these are irrational root because
`√(41)` is irrational.

Hence, The given function has 1 rational root and 2 irrational roots.