If A = {x ∈ Z : x² − 7x + 12 = 0} and B = {3, 4}, which conclusion is correct?
Answer and explanation
Correct answer: A = B
Factor the quadratic expression as x² − 7x + 12 = (x − 3)(x − 4). Therefore the equation is satisfied when x = 3 or x = 4. Both values are integers, so A = {3, 4}. Since B is also {3, 4}, the two sets contain exactly the same elements and are equal. The numbers 7 and 12 are coefficients and are not the solutions themselves. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
Factor the quadratic expression as x² − 7x + 12 = (x − 3)(x − 4). Therefore the equation is satisfied when x = 3 or x = 4. Both values are integers, so A = {3, 4}. Since B is also {3, 4}, the two sets contain exactly the same elements and are equal. The numbers 7 and 12 are coefficients and are not the solutions themselves. Thus option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
