Answer:
f(x) = (x -2)(x -1+3i)(x -1-3i)
Step-by-step explanation:
You can use synthetic division to find the remaining quadratic factor in the cubic. Then any of the usual means of solving the quadratic will help you find its linear factors.
In the attached, I show the synthetic division, the factoring to real numbers, and the solution that finds the complex linear factors by completing the square.
Of course, you know that for zeros a, b, and c, the linear factors are ...
f(x) = (x -a)(x -b)(x -c)
Here, we have a=2, b=1-3i, c=1+3i.
f(x) = (x -2)(x -1+3i)(x -1-3i)
25% 3/10 1/3 and 37.5%
.25,.30,.33,.375
Answer:
140
Step-by-step explanation:
The arithmetic series is 5, 7, 9, 11, ........., 23.
First u have to determine the no. of terms that can be done by using
Tₙ = [a + (n - 1)d]
Tₙ-------nth term
a---------first term
n---------no.of terms in the series
d---------common difference
here a = 5,d = 2.
let it contain n terms Tₙ= [a + (n-1)d]
Substitute Tₙ, a, and d in the equation
23 = 5 + (n - 1)2
Subtract 5 from each side.
18 = (n-1)2
Divide each side by 2
(n - 1) = 9
Add 1 to each side
n = 9 + 1 = 10
The sum of the arithmetic sequence formula: Sₙ= (n/2)[2a+(n-1)d]
Substitute Sₙ, a, n and d in the equation
Sₙ= (10/2)[2(5) + (10-1)2]
Sₙ= (5)[10 + (9)2]
Sₙ= 5[10 + 18]
Sₙ= 5[28] = 140
Therefore the sum of the arithmetic sequence is 140.
Answer:
x = -7 or x = 2/3
Step-by-step explanation:
I'm assuming you meant solve for x when f(x) = 0.
f(x) = 3x(x + 7) - 2(x + 7)
0 = (x + 7)(3x - 2) -- Both terms have a common factor of (x + 7) so we can group them
x + 7 = 0 or 3x - 2 = 0 -- Use ZPP
x = -7 or x = 2/3 -- Solve
Answer:
list the integers within the interval
Step-by-step explanation:
Greater than or equal to 8, so 8 is part of this list.
Less than 16, so 16 is not in this list.
