Answer:
I bet you're smarter than me so you can figure it out
Step-by-step explanation:
good thing you aint like me
Let the price of each shrub be x 4x + 17.50 = 53.50 4x = 53.50 - 17.50 x = 36/4 = <span>$9</span>
Answer:
![\displaystyle P(x)=-\frac{1}{2}(x^2+2x+10)(x-2)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20P%28x%29%3D-%5Cfrac%7B1%7D%7B2%7D%28x%5E2%2B2x%2B10%29%28x-2%29)
Step-by-step explanation:
<u>Factored Form Of Polynomials
</u>
If we know the roots of a polynomial as
![\alpha _1,\alpha _2,\alpha _3](https://tex.z-dn.net/?f=%5Calpha%20_1%2C%5Calpha%20_2%2C%5Calpha%20_3)
the polynomial can be expressed in factored form as
![a(x-\alpha _1)(x-\alpha _2)(x-\alpha _3)](https://tex.z-dn.net/?f=a%28x-%5Calpha%20_1%29%28x-%5Calpha%20_2%29%28x-%5Calpha%20_3%29)
We are given two of the three roots of the polynomial:
![\alpha _1=1-3i](https://tex.z-dn.net/?f=%5Calpha%20_1%3D1-3i)
![\alpha _2=2](https://tex.z-dn.net/?f=%5Calpha%20_2%3D2)
The other root must be the conjugate of the complex root:
![\alpha _3=1+3i](https://tex.z-dn.net/?f=%5Calpha%20_3%3D1%2B3i)
Recall the product of two complex conjugate numbers is
![(1-3i)(1+3i)=1^2-(3i)^2=1+9=10](https://tex.z-dn.net/?f=%281-3i%29%281%2B3i%29%3D1%5E2-%283i%29%5E2%3D1%2B9%3D10)
The required polynomial is
![P(x)=a\left[ x-(1-3i)\right ]\left[ x-(1+3i)\right ](x-2)](https://tex.z-dn.net/?f=P%28x%29%3Da%5Cleft%5B%20x-%281-3i%29%5Cright%20%5D%5Cleft%5B%20x-%281%2B3i%29%5Cright%20%5D%28x-2%29)
![P(x)=a(x^2+2x+10)(x-2)](https://tex.z-dn.net/?f=P%28x%29%3Da%28x%5E2%2B2x%2B10%29%28x-2%29)
This is the factored form of the polynomial where only real numbers appear
We need to find the value of a, such as
![P(0)=10](https://tex.z-dn.net/?f=P%280%29%3D10)
![P(0)=a(0^2+2(0)+10)(0-2)=10](https://tex.z-dn.net/?f=P%280%29%3Da%280%5E2%2B2%280%29%2B10%29%280-2%29%3D10)
![-20a=10](https://tex.z-dn.net/?f=-20a%3D10)
Thus the value of a is
![\displaystyle a=-\frac{1}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%3D-%5Cfrac%7B1%7D%7B2%7D)
The expression of the required polynomial is
![\boxed{P(x)=-\frac{1}{2}(x^2+2x+10)(x-2)}](https://tex.z-dn.net/?f=%5Cboxed%7BP%28x%29%3D-%5Cfrac%7B1%7D%7B2%7D%28x%5E2%2B2x%2B10%29%28x-2%29%7D)
Answer:
<h2><em><u>ᎪꪀsωꫀᏒ</u></em></h2>
=> 5/7
Step-by-step explanation:
2/7 + 3/7
=> 5/7