According to Vieta's Formulas, if
![x_1,x_2](https://tex.z-dn.net/?f=x_1%2Cx_2)
are solutions of a given quadratic equation:
Then:![a(x-x_1)(x-x_2)](https://tex.z-dn.net/?f=a%28x-x_1%29%28x-x_2%29)
is the completely factored form of
![ax^2+bx+c](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc)
.
If choose
![x=d^2](https://tex.z-dn.net/?f=x%3Dd%5E2)
, then:
![\displaystyle x^2-8x+16=0\\\\x_{1,2}= \frac{8\pm \sqrt{64-64} }{2}=4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E2-8x%2B16%3D0%5C%5C%5C%5Cx_%7B1%2C2%7D%3D%20%5Cfrac%7B8%5Cpm%20%20%5Csqrt%7B64-64%7D%20%7D%7B2%7D%3D4%20)
So, according to Vieta's formula, we can get:
![x^2-8x+16=(x-4)(x-4)= (x-4)^2](https://tex.z-dn.net/?f=x%5E2-8x%2B16%3D%28x-4%29%28x-4%29%3D%20%28x-4%29%5E2)
But
![x=d^2](https://tex.z-dn.net/?f=x%3Dd%5E2)
:
To calculate the relative vector of B we have to:
![P_B=\left[\begin{array}{ccc}3\\3\\-2\\3/2\end{array}\right]](https://tex.z-dn.net/?f=P_B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C3%5C%5C-2%5C%5C3%2F2%5Cend%7Barray%7D%5Cright%5D)
The coordenates of:
, with respect to B satisfy:
![C_1(1)+C_2(2t)+C_3(-2+4t^2)+C_4(-12t+8t^3)= 7-12t-8t^2+12t^3](https://tex.z-dn.net/?f=C_1%281%29%2BC_2%282t%29%2BC_3%28-2%2B4t%5E2%29%2BC_4%28-12t%2B8t%5E3%29%3D%207-12t-8t%5E2%2B12t%5E3)
Equating coefficients of like powers of t produces the system of equation:
![\left \{ {C_1-2C_3=7} \atop {2C_2-12C_4=-12} \right. \\\left \{ {{4C_3=-8} \atop {8C_4=12}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7BC_1-2C_3%3D7%7D%20%5Catop%20%7B2C_2-12C_4%3D-12%7D%20%5Cright.%20%5C%5C%5Cleft%20%5C%7B%20%7B%7B4C_3%3D-8%7D%20%5Catop%20%7B8C_4%3D12%7D%7D%20%5Cright.)
After solving this system, we have to:
![C_1=3\\C_2= 3\\C_3= -2\\C_4= \frac{3}{2}](https://tex.z-dn.net/?f=C_1%3D3%5C%5CC_2%3D%203%5C%5CC_3%3D%20-2%5C%5CC_4%3D%20%5Cfrac%7B3%7D%7B2%7D)
And the result is:
![P_B=\left[\begin{array}{ccc}3\\3\\-2\\3/2\end{array}\right]](https://tex.z-dn.net/?f=P_B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C3%5C%5C-2%5C%5C3%2F2%5Cend%7Barray%7D%5Cright%5D)
Learn more: brainly.com/question/16850761
Answer:
C. Many ang sagot............
Answer:
it is the sum of the initial amount and the additional amount after d days
Step-by-step explanation:
yw!!.
Answer:
4x^2+6x-20=0
Step-by-step explanation: