Answer:
B. 4 imaginary; 1 real
Step-by-step explanation:
Given the polynomial:
x^5 + 7*x^4 + 2*x^3 + 14*x^2 + x + 7
it can be reordered as follows
(x^5 + 2*x^3 + x ) + (7*x^4 + 14*x^2 + 7)
Taking greatest common factor at each parenthesis
x*(x^4 + 2*x^2 + 1) + 7*(x^4 + 2*x^2 + 1)
Taking again the greatest common factor
(x + 7)*(x^4 + 2*x^2 + 1)
Replacing x^2 = y in the second parenthesis
(x + 7)*(y^2 + 2*y + 1)
(x + 7)*(y + 1)^2
Coming back to x variable
(x + 7)*(x^2 + 1)^2
There are two options to find the roots
(x + 7) = 0
or
(x^2 + 1)^2 = 0 which is the same that (x^2 + 1) = 0
In the former case, x = -7 is the real root. In the latter, (x^2 + 1) = 0 has no real solution. Therefore, there is only 1 real root in the polynomial.
Answer:
True
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 270°
a point (x, y ) → (y, - x )
Answer:
The correct answer is 5.
Step-by-step explanation:
This is because if you divide 10 by 2 and -15 by 3
you get 5. Now to double check, you can do 10/5 and -15/5
This will give you 2, -3, which is the coordinates.
Hope this helps!
You have already done half of it. Now substitute for x1 = 4 and y = 5
y - 5 = 6/7(x - 4)
Multiply everything by 7 to remove fractions
7y - 35 = 6(x - 4)
7y - 35 = 6x - 24
-6x + 7y = -24 + 35
-6x + 7y = 11
Some people prefer a positive number in front of x so multiply by -1
6x - 7y = -11
You can check the answer by testing it works for both of the original points
6x4 - 7x5 = 24 - 35 = -11 true
6x-3 - 7x-1 = -18 - -7 = -11 true
