Each question is followed by two statements ...
1. Each question is followed by two statements A and B. Answer each question using the following instructions.
Mark (1) if the question can be answered by using statement A alone but not by using statement B alone.
Mark (2) if the question can be answered by using statement B alone but not by using statement A alone.
Mark (3) if the question can be answered by using both the statements
together but not by using either of the statements alone.
Mark (4) if the question cannot be answered on the basis of the two statements.
What is the difference in the cubes of the roots of the quadratic equation ax2 + bx + c = 0?
1. Sum of the roots of the quadratic equation is known.
2. Product of the roots of the quadratic equation is known.
Each question is followed by two statements A and B. Answer each ques...
Each question is followed by two statements A and B. Answer each ques...
Problem Analysis:
We are given a quadratic equation ax^2 + bx + c = 0, and we need to find the difference in the cubes of the roots of the equation.

Let the roots of the equation be α and β.

We need to find (α^3 - β^3).

Statement Analysis:
Statement A: Sum of the roots of the quadratic equation is known.
Statement B: Product of the roots of the quadratic equation is known.

Case Analysis:
Let's analyze the possible cases based on the statements:
1. If we know the sum of the roots (Statement A) but not the product of the roots (Statement B), we cannot determine the difference in the cubes of the roots. This is because the difference in the cubes of the roots depends on both the sum and the product of the roots.
2. If we know the product of the roots (Statement B) but not the sum of the roots (Statement A), we cannot determine the difference in the cubes of the roots. Similar to the previous case, the difference in the cubes of the roots depends on both the sum and the product of the roots.
3. If we know both the sum of the roots (Statement A) and the product of the roots (Statement B), we can determine the difference in the cubes of the roots. This is because we can express the difference in the cubes of the roots in terms of the sum and the product of the roots.

Solution:
Since we can determine the difference in the cubes of the roots using both Statement A and Statement B, the answer is (3).
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Each question is followed by two statements A and B. Answer each questionusing the following instructions.Mark (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark (2) if the question can be answered by using statement B alone but not by using statement A alone.Mark (3) if the question can be answered by using both the statementstogether but not by using either of the statements alone.Mark (4) if the question cannot be answered on the basis of the two statements.What is the difference in the cubes of the roots of the quadratic equation ax2 + bx + c = 0? Sum of the roots of the quadratic equation is known. Product of the roots of the quadratic equation is known.Correct answer is '3'. Can you explain this answer?
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