A = { x : x ∈ R , x 2 = 16 and 2 x = 6 } can be represented in the roster form as _________ . Options: A . &nbspA = {} B . &nbspA = { 14, 3, 4 } C . &nbspA = { 3 } D . &nbspA = { 4 }

A={x:x∈R, x2=16 and 2x=6} can be represented in the roster

Question

A = {x : x \in R, x^{2} = 16 and 2 x = 6}

can be represented in the roster form as _________ .

Options:

A . A = {}

B . A = { 14, 3, 4 }

C . A = { 3 }

D . A = { 4 }

Answer: Option A
:
A

x^{2} = 16 \Rightarrow x = \pm 4

2 x = 6 \Rightarrow x = 3

There is no value of

x

which satisfies both the givenequations. The set A is an empty set or a null set.
Thus, A = {}.

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