What are the twin prime numbers of 99 -199
1 answer:
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Answer:
2, 2, 4, 6, 4
Step-by-step explanation:
Fundamental Theorem of Algebra states that 'An 'n' degree polynomial will have n number of real roots'.
1. The polynomial is given by
So, on simplifying we get that, .
Since, degree of polynomial is 5, it will have 5 roots.
This gives us that the roots of the equation are x = 0, -2, 2, 4i and -4i
So, the number of complex roots are 2.
2. The polynomial is given by
Since, degree of polynomial is 4, it will have 4 roots.
Equating them both by zero, and
gives that the roots of the polynomial are x = 2i, -2i, -5, -5.
So, the number of complex roots are 2.
3. The polynomial is given by
Since, degree of polynomial is 6, it will have 6 roots.
On simplifying, we get that the real roots of the polynomial are x = -1.75 and x = 4.28.
So, the number of complex roots are 6-2 = 4.
4. The polynomial is given by
Since, degree of polynomial is 7, it will have 7 roots.
On simplifying, we get that the only real root of the polynomial is x = -2.
So, the number of complex roots are 7-1 = 6.
5. The polynomial is given by
Since, degree of polynomial is 5, it will have 5 roots.
Simplifying the equation gives
Equating each to 0, we get the real roots of the polynomial is
So, the number of complex roots are 5-1 = 4
Question 3)
Given
The point (1, -5)
The slope m = -5/6
Using the point-slope form of the equation of a line
where
- m is the slope of the line
- (x₁, y₁) is the point
In our case:
- m = -5/6
- (x₁, y₁) = (1, -5)
substituting the values m = -5/6 and the point (1, -5) in the point-slope form of the equation of the line
Thus, the point-slope form of the equation of the line is:
Question 4)
Given
The point (-1, 5)
The slope m = -7/2
In our case:
- m = -7/2
- (x₁, y₁) = (-1, 5)
substituting the values m = -7/2 and the point (-1, 5) in the point-slope form of the equation of the line
Thus, the point-slope form of the equation of the line is: