to get the slope of any line, all we need is two points off of it.
so let's see hmmmmmmm this line passes through (0, 1) and hmmmm (4, -2)
![\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-2-1}{4-0}\implies \cfrac{-3}{4}\implies -\cfrac{3}{4}](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B0%7D~%2C~%5Cstackrel%7By_1%7D%7B1%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B4%7D~%2C~%5Cstackrel%7By_2%7D%7B-2%7D%29%20%5C%5C%5C%5C%5C%5C%20slope%20%3D%20m%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Brise%7D%7B%20y_2-%20y_1%7D%7D%7B%5Cstackrel%7Brun%7D%7B%20x_2-%20x_1%7D%7D%5Cimplies%20%5Ccfrac%7B-2-1%7D%7B4-0%7D%5Cimplies%20%5Ccfrac%7B-3%7D%7B4%7D%5Cimplies%20-%5Ccfrac%7B3%7D%7B4%7D)
Solution:
The given Polynomial is :
![f(x) = 5x^4 + 4x^3 - 2x^2 + 2x + 4=5( x^4 + \frac{4}{5}x^3 - \frac{2}{5}x^2 + \frac{2}{5}x + \frac{4}{5})](https://tex.z-dn.net/?f=f%28x%29%20%3D%205x%5E4%20%2B%204x%5E3%20-%202x%5E2%20%2B%202x%20%2B%204%3D5%28%20x%5E4%20%2B%20%5Cfrac%7B4%7D%7B5%7Dx%5E3%20-%20%5Cfrac%7B2%7D%7B5%7Dx%5E2%20%2B%20%5Cfrac%7B2%7D%7B5%7Dx%20%2B%20%5Cfrac%7B4%7D%7B5%7D%29)
By Rational Root theorem the of Zeroes of the Polynopmial are:
![\pm\frac{1}{5},\pm\frac{2}{5},\pm\frac{4}{5},\pm1,\pm2,\pm4](https://tex.z-dn.net/?f=%5Cpm%5Cfrac%7B1%7D%7B5%7D%2C%5Cpm%5Cfrac%7B2%7D%7B5%7D%2C%5Cpm%5Cfrac%7B4%7D%7B5%7D%2C%5Cpm1%2C%5Cpm2%2C%5Cpm4)
But , ![f(\pm\frac{1}{5},\pm\frac{2}{5},\pm\frac{4}{5},\pm1,\pm2,\pm4)\neq 0](https://tex.z-dn.net/?f=f%28%5Cpm%5Cfrac%7B1%7D%7B5%7D%2C%5Cpm%5Cfrac%7B2%7D%7B5%7D%2C%5Cpm%5Cfrac%7B4%7D%7B5%7D%2C%5Cpm1%2C%5Cpm2%2C%5Cpm4%29%5Cneq%200)
So, no root of this polynomial is real.
Therefore, All the four roots of Polynomial are imaginary.
So, we can't say whether the number k=2, is an upper or lower bound of the polynomial
.
Answer: 1.5
Step-by-step explanation:
Answer:
His Debit Card
Step-by-step explanation:
Because whenever i go to the story with adults they are most likely to use there debit card. Or they do use there debit card