CA Foundation Exam > CA Foundation Questions > The sets V = {x / x+2=0}, R={x / x2+2x=0} and...
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The sets V = {x / x+2=0}, R={x / x2+2x=0} and S = {x : x2+x–2=0} are equal to one another if x is equal to
- a)–2
- b)2
- c)½
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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The sets V = {x / x+2=0}, R={x / x2+2x=0} and S = {x : x2+x2=0} are eq...
To determine if the sets V, R, and S are equal to each other, we need to find the values of x that satisfy the given conditions for each set.
Set V: {x / x^2 = 0}
To find the values of x that satisfy this condition, we need to solve the equation x^2 = 0.
The only value of x that satisfies this equation is x = 0.
Set R: {x / x^2 + 2x = 0}
To find the values of x that satisfy this condition, we need to solve the equation x^2 + 2x = 0.
Factoring out an x from the equation, we get x(x + 2) = 0.
Setting each factor equal to zero, we find two possible values for x: x = 0 and x = -2.
Set S: {x / x^2 + x^2 = 0}
To find the values of x that satisfy this condition, we need to solve the equation x^2 + x^2 = 0.
Combining like terms, we get 2x^2 = 0.
Dividing both sides of the equation by 2, we get x^2 = 0.
As we saw in set V, the only value of x that satisfies this equation is x = 0.
Comparing the sets V, R, and S, we can see that the only value of x that appears in all three sets is x = 0.
Therefore, the correct answer is option 'A', x = 0.
Set V: {x / x^2 = 0}
To find the values of x that satisfy this condition, we need to solve the equation x^2 = 0.
The only value of x that satisfies this equation is x = 0.
Set R: {x / x^2 + 2x = 0}
To find the values of x that satisfy this condition, we need to solve the equation x^2 + 2x = 0.
Factoring out an x from the equation, we get x(x + 2) = 0.
Setting each factor equal to zero, we find two possible values for x: x = 0 and x = -2.
Set S: {x / x^2 + x^2 = 0}
To find the values of x that satisfy this condition, we need to solve the equation x^2 + x^2 = 0.
Combining like terms, we get 2x^2 = 0.
Dividing both sides of the equation by 2, we get x^2 = 0.
As we saw in set V, the only value of x that satisfies this equation is x = 0.
Comparing the sets V, R, and S, we can see that the only value of x that appears in all three sets is x = 0.
Therefore, the correct answer is option 'A', x = 0.
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The sets V = {x / x+2=0}, R={x / x2+2x=0} and S = {x : x2+x2=0} are equal to one another if x is equal toa)2b)2c)d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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