Question

$A=\{x:x\in R,x^2=16\text{and}2x=6\}$ can be represented in the roster form as _________ .

• A. $A=\{14,3,4\}$
• B. $A=\left\{3\right\}$
• C. $A=\left\{4\right\}$
• D. $A=\left\{\right\}$

Answer 1

The correct option is D

$A=\left\{\right\}$

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

$A$ is the set of common solutions of equations $x^2=16\text{and}2x=6$
As $x^2=16\Rightarrow x=\pm 4$
ans $2x=6\Rightarrow x=3$

There is no value of $x$ which satisfies both the given equations.
The set $A$ is an empty set or a null set.

Thus, $A=\left\{\right\}$.