Answer:
Option B
Step-by-step explanation:
Complex roots occur as conjugate pairs so the third root is -3 - i ( note that the sign changes from + to -).
So in factor form we have:-
(x - 2)(x - (-3 + i))(x - (-3 - i)) = 0 Let's expand the last 2 factors first:-
(x - (-3 + i))(x - (-3 - i))
= (x + 3 - i)(x + 3 + i)
= x^2 + 3x +ix + 3x + 9 + 3i - ix - 3i - i^2
= x^2 + 6x + 9 - (-1)
= x^2 + 6x + 10
Now multiplying by (x - 2):-
(x - 2)(x^2 + 6x + 10) = 0
x^3 + 6x^2 + 10x - 2x^2 - 12x - 20 = 0
x^3 + 4x^2 - 2x - 20 = 0 (answer)
Option B
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-10})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ 10=\sqrt{[x-(-6)]^2+[-4-(-10)]^2}\implies 10=\sqrt{(x+6)^2+(-4+10)^2} \\\\\\ 10^2=(x+6)^2+(6)^2\implies 100=x^2+12x+36+36 \\\\\\ 100=x^2+12x+72\implies 0=x^2+12x-28 \\\\\\ 0=(x+14)(x-2)\implies x= \begin{cases} -14\\ \boxed{2} \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20A%28%5Cstackrel%7Bx_1%7D%7B-6%7D~%2C~%5Cstackrel%7By_1%7D%7B-10%7D%29%5Cqquad%20B%28%5Cstackrel%7Bx_2%7D%7Bx%7D~%2C~%5Cstackrel%7By_2%7D%7B-4%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%2010%3D%5Csqrt%7B%5Bx-%28-6%29%5D%5E2%2B%5B-4-%28-10%29%5D%5E2%7D%5Cimplies%2010%3D%5Csqrt%7B%28x%2B6%29%5E2%2B%28-4%2B10%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%2010%5E2%3D%28x%2B6%29%5E2%2B%286%29%5E2%5Cimplies%20100%3Dx%5E2%2B12x%2B36%2B36%20%5C%5C%5C%5C%5C%5C%20100%3Dx%5E2%2B12x%2B72%5Cimplies%200%3Dx%5E2%2B12x-28%20%5C%5C%5C%5C%5C%5C%200%3D%28x%2B14%29%28x-2%29%5Cimplies%20x%3D%20%5Cbegin%7Bcases%7D%20-14%5C%5C%20%5Cboxed%7B2%7D%20%5Cend%7Bcases%7D)
because B is on the IV Quadrant, the x-coordinate must be positive.
The answer is
200%Why? --- A change from 12 to 36 represents a positive change (increase) of 200%
Use the formula found below on this webpage to find the percent change by replacing the given values:
Percent change = [(12 - 36) / 12] x 100 = 200 % (increase)
Where: 12 is the old value and 36 is the new value. In this case we have a positive change (increase) of 200 percent because the new value is greater than the old value.
Hope this helps. :)
~
Anonymous
