Answer:
X1=-4+4i
X2=-4-4i
Step-by-step explanation:
X^2+8x+32=0
Δ=b^2-4ac=8^2-4(32)=-64<0
X1=(-b-i√Δ) /2a=(-8-8i)/2=-4-4i
X2=(-b+i√Δ) /2a=(-8+8i)/2=-4+4i
Answer: 10 visit
Step-by-step explanation:
Given
45 Points earned by signing up
11.5 points earned for each visit to the theatre
160 points are needed for a movie ticket
Suppose, after x visit he gets enough points to buy a movie ticket
![\therefore 160=45+11.5x\\\Rightarrow 115=11.5x\\\Rightarrow x=10](https://tex.z-dn.net/?f=%5Ctherefore%20160%3D45%2B11.5x%5C%5C%5CRightarrow%20115%3D11.5x%5C%5C%5CRightarrow%20x%3D10)
So, after 10th visit, he earns a movie ticket
Step-by-step explanation:
The root is
-sqr root of 5.
First, we put these roots in the forn of
![(x - a)](https://tex.z-dn.net/?f=%28x%20-%20a%29)
where a is the root
So we have
![(x - ( - 2))(x - \sqrt{5} )(x - \frac{10}{3} )](https://tex.z-dn.net/?f=%28x%20-%20%28%20-%202%29%29%28x%20-%20%20%5Csqrt%7B5%7D%20%29%28x%20-%20%20%5Cfrac%7B10%7D%7B3%7D%20%29)
![(x + 2)(x - \sqrt{5} )(3x - 10)](https://tex.z-dn.net/?f=%28x%20%2B%202%29%28x%20-%20%20%5Csqrt%7B5%7D%20%29%283x%20-%2010%29)
![(3 {x}^{2} - 4x - 20)(x - \sqrt{5} )](https://tex.z-dn.net/?f=%283%20%7Bx%7D%5E%7B2%7D%20%20-%204x%20-%2020%29%28x%20-%20%20%5Csqrt%7B5%7D%20%29)
To get rid of that square root, let have another root that js the conjugate posive root of 5.
![(3 {x}^{2} - 4x - 20)(x - \sqrt{5} )(x + \sqrt{5} )](https://tex.z-dn.net/?f=%283%20%7Bx%7D%5E%7B2%7D%20%20-%204x%20-%2020%29%28x%20-%20%20%5Csqrt%7B5%7D%20%29%28x%20%2B%20%20%5Csqrt%7B5%7D%20%29)
![(3 {x}^{2} - 4x - 20)(x {}^{2} + 5)](https://tex.z-dn.net/?f=%283%20%7Bx%7D%5E%7B2%7D%20%20-%204x%20-%2020%29%28x%20%7B%7D%5E%7B2%7D%20%20%2B%205%29)
Which will gives us a rational coeffeicent of degree 4.
Why we didn't do
![(x - \sqrt{5} )](https://tex.z-dn.net/?f=%28x%20-%20%20%5Csqrt%7B5%7D%20%29)
?
Because
![(x - \sqrt{5} ) {}^{2} = {x}^{2} - 2 \sqrt{5} + 5](https://tex.z-dn.net/?f=%28x%20-%20%20%5Csqrt%7B5%7D%20%29%20%7B%7D%5E%7B2%7D%20%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20-%202%20%5Csqrt%7B5%7D%20%20%2B%205)
If we foiled out we will still have a irrational coeffceint.