These three roots are sufficient to enable us to form a 3rd degree polynomial:
f(x) = (x+4)(x-4)(x-2) = (x^2 - 16)(x-2) = x^3 - 2x^2 - 16x + 32 (answer)
Answer:
14x+6
Step-by-step explanation:
Multiply 7x by 2 which gets you 14x and multiply 3 by 2 which is 6.
Im pretty sure its the last one. Length AB = Length A'B'
Answer:
A) The coordinates of the fourth vertex are:
1) x-coordinate:
![x=2](https://tex.z-dn.net/?f=x%3D2)
2) y-coordinate:
![y=-1](https://tex.z-dn.net/?f=y%3D-1)
B) The point of intersection of the diagonals is: ![(2,1)](https://tex.z-dn.net/?f=%282%2C1%29)
Step-by-step explanation:
We need to remember that the diagonals of a parallelogram intersect each other at a half-way point and the midpoint of each diagonal is the same.
The midpoint formula is:
![M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})](https://tex.z-dn.net/?f=M%3D%28%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%5Cfrac%7By_1%2By_2%7D%7B2%7D%29)
Since:
![M_{AC}=M_{BD}](https://tex.z-dn.net/?f=M_%7BAC%7D%3DM_%7BBD%7D)
We can find the coordinates of the fourth vertex
through these procedure:
1) x-coordinate:
![\frac{1+3}{2}=\frac{2+x}{2}\\\\2(2)=x\\\\4-2=x\\\\x=2](https://tex.z-dn.net/?f=%5Cfrac%7B1%2B3%7D%7B2%7D%3D%5Cfrac%7B2%2Bx%7D%7B2%7D%5C%5C%5C%5C2%282%29%3Dx%5C%5C%5C%5C4-2%3Dx%5C%5C%5C%5Cx%3D2)
2) y-coordinate:
![\frac{0+2}{2}=\frac{3+y}{2}\\\\1(2)-3=y\\\\y=-1](https://tex.z-dn.net/?f=%5Cfrac%7B0%2B2%7D%7B2%7D%3D%5Cfrac%7B3%2By%7D%7B2%7D%5C%5C%5C%5C1%282%29-3%3Dy%5C%5C%5C%5Cy%3D-1)
Therefore, fourth vertex is
Since the point of intersection of the diagonals is the midpoint of a diagonal (Remember that
), this is:
![M_{AC}=M_{BD}=(\frac{1+3}{2},\frac{0+2}{2})\\\\M_{AC}=M_{BD}=(2,1)](https://tex.z-dn.net/?f=M_%7BAC%7D%3DM_%7BBD%7D%3D%28%5Cfrac%7B1%2B3%7D%7B2%7D%2C%5Cfrac%7B0%2B2%7D%7B2%7D%29%5C%5C%5C%5CM_%7BAC%7D%3DM_%7BBD%7D%3D%282%2C1%29)
Therefore, the point of intersection of the diagonals is ![(2,1)](https://tex.z-dn.net/?f=%282%2C1%29)