Answer:
-3.5 < -3
Step-by-step explanation:
-3 is greater than -3.5
Answer:
Simplest function is f(x) = 2x - 1
Step-by-step explanation:
When a function has a zero, simply put, that point is where the graph goes through the x-axis. At this point, the y value is 0.
If a function has a 0 of 1/2, that translates to x = 1/2 and also (1/2, 0). That means that y = 0 when x = 1/2.
If x = 1/2 and is a zero, then x - 1/2 = 0 and 2x - 1 = 0 (notice that y = 0 here and solving for x would get you right back to x = 1/2).
The simplest function with a zero of 1/2 is
f(x) = 2x - 1
You know it is true that the zero is 1/2 for two reasons. First one is to set the right side equal to 0 and solve for x.
The second one is to graph the line y = 2x - 1 and see that it goes through the x axis at 1/2 where y = 0.
The roots routine will return a column vector containing the roots of a polynomial. The general syntax is
z = roots(p)
where p is a vector containing the coefficients of the polynomial ordered in descending powers.
Given a vector
which describes a polynomial
we construct the companion matrix (which has a characteristic polynomial matching the polynomial described by p), and then find the eigenvalues of it (which are the roots of its characteristic polynomial)
Example
Here is an example of finding the roots to the polynomial
--> roots([1 -6 -72 -27])
ans =
12.1229
-5.7345
-0.3884
Answer:
x²+y²+4x-21=0
Step-by-step explanation:
(x-h)²+(y-k)²=r²
(x--2)²+(y-0)²=(5)²
(x+2)²+y²=25
x²+4x+4+y²=25
x²+y²+4x-21=0
