f (x), has (x-7) and (x+4i) as factors. F(X)=2x^5-13x^4+22x^3-187x^2-160x+336 what is the total number of real numbers of real zeros of f(X)
Answers
Answer: 3
Step-by-step explanation:
(x + 4i) is a root which means its conjugate (x - 4i) is also a root
(x + 4i)(x - 4i) = x² + 16
Use Long Division for 2x⁵ - 13x⁴ + 22x³ - 187x² - 160x + 336 ÷ x² + 16
2x³ - 13x² - 10x + 21
x² + 16 ) 2x⁵ - 13x⁴ + 22x³ - 187x² - 160x + 336
- (2x⁵ + 0x⁴ + 32x³) ↓ ↓ ↓
-13x⁴ - 10x³ - 187x² ↓ ↓
- (-13x⁴ +0x³ - 208x²) ↓ ↓
-10x³ + 21x² - 160x ↓
- (-10x³ + 0x² - 160x) ↓
21x² + 0x + 336
- (21x² + 0x + 336)
0
Use Synthetic Division to divide (x - 7) by the reduced polynomial (2x³ - 13x² - 10x + 21)
7 | 2 -13 -10 21
| ↓ 14 7 -21
2 1 -3 0 ← remainder is 0
Use grouping to factor the reduced polynomial (2x² + x - 3)
2x² - 2x + 3x - 3
= 2x(x - 1) +1(x - 1)
= (2x + 1)(x - 1)
The factors are: (x - 7) (2x + 1) (x - 1) (x + 4i) (x - 4i)
The first 3 are real roots and the last 2 are complex roots
The zeros of a polynomial function are the factors of the function.
The number of real zeros of f(x) is 3
The function is given as:
Two of the factors are given as:
x - 7 ad x + 4i
The factor x + 4i is a complex factor.
If a polynomial function has a complex factor, then the conjugate of the complex factor is also a factor of the polynomial.
This means that f(x) has 2 complex factors
The degree of the polynomial is 5.
So, the number (r) of real zeros is the difference between the degree of the polynomial and the number of complex factors.
This gives
Hence, the number of real zeros of f(x) is 3
Read more about zeros of polynomials at:
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Solve for the line from the graph, thank you!
Answers
So, there are 1000 milligrams in one gram, making the 4000 mgs equal to 4 grams.
There are 1000 grams in one kilogram, so 4 kilograms is equal to 4000 grams.
4000 =/= 4
So, 4 kilograms and 4000 milligrams are not equal.
Answers
Given . . . 20 = k 4
k = 20/4 = 5 .
x = −2, x = 0
x = 2, x = 0
x = 0, x = 1 over 2
Answers
|x| makes x posotive
5|2x-2|+8=18
minus 8 both sides
5|2x-2|=10
divide both sides by 5
|2x-2|=2
assume
2x-2=2 and 2x-2=-2
2x-2=2
add 2
2x=4
divide 2
x=2
2x-2=-2
add 2
2x=0
x=0
x=0 or x=2
3rd choice
Answer:
C. x = 2, x = 0
Step-by-step explanation:
Answers
-+-=+
Answers
Answer:
271.6 or 272
Step-by-step explanation:
815 is being times by 3
so we do the opposite
815/3 on both sides
3x/3=0
drop the x
then do 815/3
= x= 271.6 or 272
Final answer:
To simplify the equation 815 = 3x, divide both sides of the equation by 3 to isolate the variable x. The solution to the equation is x = 271.
Explanation:
To simplify the equation 815 = 3x, we need to isolate the variable x on one side of the equation.
To do this, we divide both sides of the equation by 3 to cancel out the coefficient of x.
This gives us x = 815/3. Performing the division, we get x = 271.
Therefore, the solution to the equation is x = 271.
B:X=-11 and X=1
C:X=11 and x= -1
D:x=-11 and x=-1
I need help asap it’s algebra 2 please help!
Answers
Answer:
it too hard
Step-by-step explanation:
4×5x=24
5x=24÷4
5x=6
x=6÷5
x=1.2