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Question :
Find the zeros of quadratic polynomial for (6x^{2} + 1) / (6x -2) and verify the relationship between the zeros and Co efficient
Solution :
(6x^{2} + 1) / (6x -2) = 0
6x^{2} + 1 = 0
6x^{2} = -1
x^{2} = -1/6
x = √(-1/6)
The roots are not real. Hence we cannot verify the relationship.
Question 2 :
Let f = {(x, y) | x, y ∈ N and y = 2x} be a relation on ℕ. Find the domain, co-domain and range. Is this relation a function?
Solution :
Since x and y ∈ N,
x = 1 if x = 2 if x = 3 if x = 4
y = 2 y = 4 y = 6 y = 8
f = {(1, 2) (2, 4) (3, 6) (4, 8)................}
For each values of x, we get different values of y. So the given relation is a function.
Domain is the set of values of x
Domain = {1, 2, 3, 4, ............}
Co domain is the set of value of y. Since y ∈ N
Co domain = {1, 2, 3, 4, .............}
Range means the set of values of y, which are associated with x.
Range = {2, 4, 6, 8, .....}
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