![f(x) = -x^6 -x^5 - x^4 - 4x^3 - 12x^2 + 12](https://tex.z-dn.net/?f=%20f%28x%29%20%3D%20-x%5E6%20-x%5E5%20-%20x%5E4%20-%204x%5E3%20-%2012x%5E2%20%2B%2012)
There is only one change of sign, so there is only one possible positive root.
![f(-x) = -(-x)^6 -(-x)^5 - (-x)^4 - 4(-x)^3 - 12(-x)^2 + 12\\ f(-x) = -x^6 +x^5 - x^4 + 4x^3 - 12x^2 + 12](https://tex.z-dn.net/?f=f%28-x%29%20%3D%20-%28-x%29%5E6%20-%28-x%29%5E5%20-%20%28-x%29%5E4%20-%204%28-x%29%5E3%20-%2012%28-x%29%5E2%20%2B%2012%5C%5C%0Af%28-x%29%20%3D%20-x%5E6%20%2Bx%5E5%20-%20x%5E4%20%2B%204x%5E3%20-%2012x%5E2%20%2B%2012)
There are five changes of signs, so there are 5,3 or 1 possible negative roots.
The number of complex roots can be equal to 4,2 or 0 (degree of a polynomial - possible positive roots - possible negative roots)
<h3>
Answer: y = -x + 6</h3>
To get this answer, you subtract x from both sides to go from x+y = 6 to y = 6-x which rearranges to y = -x+6
Note that y = -x+6 is the same as y = -1x+6
We can compare this to y = mx+b form to see that m = -1 is the slope and b = 6 is the y intercept.
1500 divided by 100 is 15 .
Answer:
<h3>a) 9/2</h3>
Step-by-step explanation:
The formula of a slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
We have the points (2, 5) and (0, -4). Substitute:
![m=\dfrac{-4-5}{0-2}=\dfrac{-9}{-2}=\dfrac{9}{2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B-4-5%7D%7B0-2%7D%3D%5Cdfrac%7B-9%7D%7B-2%7D%3D%5Cdfrac%7B9%7D%7B2%7D)