ANSWER
A. -3, -2, 2, and 3
EXPLANATION
The given polynomial function is,
![f(x) = {x}^{4} - 13 {x}^{2} + 36](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%7Bx%7D%5E%7B4%7D%20-%2013%20%7Bx%7D%5E%7B2%7D%20%2B%2036)
To find the real roots, we equate the function to zero to obtain;
![{x}^{4} - 13 {x}^{2} + 36 = 0](https://tex.z-dn.net/?f=%7Bx%7D%5E%7B4%7D%20-%2013%20%7Bx%7D%5E%7B2%7D%20%2B%2036%20%3D%200)
We can solve this equation as a quadratic equation in
![{x}^{2}.](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D.)
Thus we rewrite the equation as,
![({x}^{2})^{2} - 13 {x}^{2} + 36 = 0](https://tex.z-dn.net/?f=%28%7Bx%7D%5E%7B2%7D%29%5E%7B2%7D%20-%2013%20%7Bx%7D%5E%7B2%7D%20%2B%2036%20%3D%200)
We split the middle term to get,
![({x}^{2})^{2} - 9 {x}^{2} - 4 {x}^{2} + 36 = 0.](https://tex.z-dn.net/?f=%28%7Bx%7D%5E%7B2%7D%29%5E%7B2%7D%20-%209%20%7Bx%7D%5E%7B2%7D%20-%204%20%7Bx%7D%5E%7B2%7D%20%2B%2036%20%3D%200.)
We factor to get,
![{x}^{2} ( {x}^{2} - 9) - 4( {x}^{2} - 9) = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%28%20%7Bx%7D%5E%7B2%7D%20-%209%29%20-%204%28%20%7Bx%7D%5E%7B2%7D%20-%209%29%20%3D%200)
We factor to get,
![( {x}^{2} - 9)( {x}^{2} - 4) = 0](https://tex.z-dn.net/?f=%28%20%7Bx%7D%5E%7B2%7D%20-%209%29%28%20%7Bx%7D%5E%7B2%7D%20-%204%29%20%3D%200)
Either
![{x}^{2} - 9 = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20-%209%20%3D%200)
or
![{x}^{2} - 4 = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20-%204%20%3D%200)
![x = \pm \sqrt{9} \: or \: x = \pm \sqrt{4}](https://tex.z-dn.net/?f=x%20%3D%20%5Cpm%20%5Csqrt%7B9%7D%20%5C%3A%20or%20%5C%3A%20x%20%3D%20%5Cpm%20%5Csqrt%7B4%7D%20)
![x = \pm3 \: or \: x = \pm2](https://tex.z-dn.net/?f=x%20%3D%20%5Cpm3%20%5C%3A%20or%20%5C%3A%20x%20%3D%20%5Cpm2)
![x=-3,-2,2,3](https://tex.z-dn.net/?f=x%3D-3%2C-2%2C2%2C3)
The correct answer is A
Problem 7
(45 pages)/(90 min) = 1/2 page per min, i.e. 1 page per 2 minutes
(60 pages)(120 min) = 1/2 page per min
Both lead to the same result, so yes they are proportional.
Their reading speed is identical.
<h3>Answer: True</h3>
Answer:i dont know
Step-by-step explanation:
Each term differs by -68 and the first term is -68, we have:
![a_{n}=a_1-68(n-1) \implies \\ a_{n}=a_1-68n+68 \implies\\ a_n=-68-68n+68 \implies \\ a_n=-68n](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_1-68%28n-1%29%20%5Cimplies%20%5C%5C%20a_%7Bn%7D%3Da_1-68n%2B68%20%5Cimplies%5C%5C%20a_n%3D-68-68n%2B68%20%5Cimplies%20%5C%5C%20a_n%3D-68n)
As an expession it's just -68n.
With every imaginary term, there are 2 complex conjugates with opposing signs. So if I had the term a+bi, the complex conjugate would be a-bi. So given your example of -1+4i, the complex conjugate would just be the opposite sign, now negative, to get -1-4i.