Answer:
There are two rational roots for f(x)
Explanation:
We are given a function
f(x) = x^6-2x^4-5x^2+6f(x)=x6−2x4−5x2+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)f(x)=(x−1)(x+1)(x2−3)
We find that f(x) (x^2-3)f(x)(x2−3) factor gives two irrational solutions as
±√3.
Hence number of rational roots are 2.
The conclusion of the research is that we reject the null hypothesis and we conclude that the bag filling machine does not work correctly at the 426 gram setting.
<h3>How to solve hypothesis testing?</h3>
We are given;
Population Mean; μ = 426
Sample mean; x' = 433
Sample size; n = 13
Standard deviation; s = 29
significance level; α = 0.05
Let us define the hypotheses;
Null Hypothesis; H₀: μ = 426 g
Alternative Hypothesis; H_a: μ < 426 g
Formula for the z-score here is;
z = (x' - μ)/(s/√n)
z = (433 - 426)/(29/√13)
z = 0.87
From online p-value from z-score calculator, we have;
p-value = 0.1922
This p-value is greater than the significance value and as such we reject the null hypothesis and we conclude that the bag filling machine does not work correctly at the 426 gram setting.
Read more about Hypothesis testing at; brainly.com/question/15980493
#SPJ1
A. The pigs use lies and deceit to control the other animals.
I think it’s B
Hope it’s correct
