Answer:
Values for alpha and beta are 0.5 and 3.
Step-by-step explanation:
2x² - 7x - 3 = 0
2x² - 7x - 3 = (2x - 1 )(x - 3)
∴ (2x - 1 )(x - 3) = 0
The only way to get zero by multiplying two values together, is if one of those values is qual to zero. Therefore, either (2x - 1 )=0, or (x - 3)=0.
If (2x - 1 )=0
∴2x=1
∴x=0.5
If (x - 3)=0
∴x=3
We have two values for x. These values represent alpha and beta.
<em>(BTW - I'm not sure from the phrasing of your question whether or not you just want to find the values or whether you want to find the sum of the values (I don't know if you used '+' to mean 'and' or 'plus'), but if you do want to find the sum, it's of course just 0.5+3= 3.5.)</em>
Let n = 0, 1, 2, 3, 4, 5, 6, 7....
When n = 0 then 0^2 + 0 = 0. n = 1 we have 1^2 + 1 = 2. And when n = 2 we have 2^2 + 2 = 6. When n= 3 we have 3^2 + 3 = 12. When n = 4 we have 4^2 + 4 = 20. When n = 5 we have 5^2 + 5 = 30. When n = 6 = 6^2 + 6 = 42. And finally when n = 7 we have 7^2 + 7 = 56. So at n = 1, 2, ...7, ... Our values are = 2, 6, 12, 20, 30, 42, and 56. It is obvious that n is always an even number. Hence n^2 + n is always an even integer for all positive integers.
When n = -1 we have (-1)^2 - 1 = 0 when n = -2 we have (-2)^2 -2 = 2. When n = -3 we have (-3)^2 - 3 = 6. When n = -4 we have (-4)^2 - 4 = 16 - 4 =12. When n =-5 we have (-5)^2 -5 = 20. When n = -6 we have (-6)^2 - 6 = 30. When n = (-7)^2 - 7 = 42. Hence n^2 + n is always even for all integers
Answer:
60 Hope this helps you :)
Step-by-step explanation:
Answer:
-2x+Y=12
Step-by-step explanation:
4x-2y=8
-4x -4x
-2y=-4x+8
-2 -2
Y= -4x/-2 + 8/-2
Y= 2x-4
M= 2
Y=mx+b
8=2 (-2) +b
8= -4+b
12=b
Y=2x+12
-2x -2x
-2x+Y=12
