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There is a question statement which is followed by two statements A and B. You have to decide whether the information provided in the two statements is sufficient for answering the question.
What is the sum of square of all the roots of the equation x4 + ax3 + cx2 +dx + e?
(A) e = 89
(B) All the roots are integers.
- a)If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.
- b)If the question can be answered by using either statement alone.
- c)If the question can be answered by using both statements together, but cannot be answered by using either statement alone.
- d)If the question cannot be answered even by using both the statements together
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
There is a question statement which is followed by two statements A a...
Question: What is the sum of the square of all the roots of the equation x^4 + ax^3 + cx^2 + dx + e?
Statement A: e = 89
Statement B: All the roots are integers.
Explanation:
To find the sum of the square of all the roots of the given equation, we need to know the values of a, c, d, and e. Let's analyze the statements one by one.
Statement A: e = 89
This statement provides the value of e, which is one of the coefficients of the equation. However, it does not provide any information about the values of a, c, and d. Without knowing these values, we cannot determine the sum of the square of all the roots. Therefore, statement A alone is not sufficient to answer the question.
Statement B: All the roots are integers.
This statement tells us that all the roots of the equation are integers. Knowing this information, we can determine the sum of the square of all the roots. Since the roots are integers, we can express the given equation as a product of linear factors:
(x - r1)(x - r2)(x - r3)(x - r4) = 0
Expanding this equation:
x^4 - (r1 + r2 + r3 + r4)x^3 + (r1r2 + r1r3 + r1r4 + r2r3 + r2r4 + r3r4)x^2 - (r1r2r3 + r1r2r4 + r1r3r4 + r2r3r4)x + r1r2r3r4 = 0
Comparing the coefficients with the given equation:
a = -(r1 + r2 + r3 + r4)
c = r1r2 + r1r3 + r1r4 + r2r3 + r2r4 + r3r4
d = -(r1r2r3 + r1r2r4 + r1r3r4 + r2r3r4)
e = r1r2r3r4
To find the sum of the square of all the roots (r1^2 + r2^2 + r3^2 + r4^2), we need the values of a, c, d, and e. Statement B alone does not provide this information. Therefore, statement B alone is not sufficient to answer the question.
Using both statements together:
Combining the information from both statements, we know that e = 89 and all the roots are integers. However, this information is still not sufficient to determine the values of a, c, and d. Without knowing these values, we cannot calculate the sum of the square of all the roots. Therefore, even when using both statements together, we cannot answer the question.
Hence, the correct answer is option C.
Statement A: e = 89
Statement B: All the roots are integers.
Explanation:
To find the sum of the square of all the roots of the given equation, we need to know the values of a, c, d, and e. Let's analyze the statements one by one.
Statement A: e = 89
This statement provides the value of e, which is one of the coefficients of the equation. However, it does not provide any information about the values of a, c, and d. Without knowing these values, we cannot determine the sum of the square of all the roots. Therefore, statement A alone is not sufficient to answer the question.
Statement B: All the roots are integers.
This statement tells us that all the roots of the equation are integers. Knowing this information, we can determine the sum of the square of all the roots. Since the roots are integers, we can express the given equation as a product of linear factors:
(x - r1)(x - r2)(x - r3)(x - r4) = 0
Expanding this equation:
x^4 - (r1 + r2 + r3 + r4)x^3 + (r1r2 + r1r3 + r1r4 + r2r3 + r2r4 + r3r4)x^2 - (r1r2r3 + r1r2r4 + r1r3r4 + r2r3r4)x + r1r2r3r4 = 0
Comparing the coefficients with the given equation:
a = -(r1 + r2 + r3 + r4)
c = r1r2 + r1r3 + r1r4 + r2r3 + r2r4 + r3r4
d = -(r1r2r3 + r1r2r4 + r1r3r4 + r2r3r4)
e = r1r2r3r4
To find the sum of the square of all the roots (r1^2 + r2^2 + r3^2 + r4^2), we need the values of a, c, d, and e. Statement B alone does not provide this information. Therefore, statement B alone is not sufficient to answer the question.
Using both statements together:
Combining the information from both statements, we know that e = 89 and all the roots are integers. However, this information is still not sufficient to determine the values of a, c, and d. Without knowing these values, we cannot calculate the sum of the square of all the roots. Therefore, even when using both statements together, we cannot answer the question.
Hence, the correct answer is option C.
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Community Answer
There is a question statement which is followed by two statements A a...
Clearly individual statements alone are not sufficient. Combining both we observe that the product of all the roots is 89. Also roots are integers and 89 is prime number hence one of the root will surely be 89 and rest of the four roots will be 1 or -1. Therefore sum of squares of all the roots = 892 + 4x12 = 7925.
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There is a question statement which is followed by two statements A and B. You have to decide whether the information provided in the two statements is sufficient for answering the question.What is the sum of square of all the roots of the equation x4 + ax3 + cx2 +dx + e?(A) e = 89(B) All the roots are integers.a)If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.b)If the question can be answered by using either statement alone.c)If the question can be answered by using both statements together, but cannot be answered by using either statement alone.d)If the question cannot be answered even by using both the statements togetherCorrect answer is option 'C'. Can you explain this answer?
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There is a question statement which is followed by two statements A and B. You have to decide whether the information provided in the two statements is sufficient for answering the question.What is the sum of square of all the roots of the equation x4 + ax3 + cx2 +dx + e?(A) e = 89(B) All the roots are integers.a)If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.b)If the question can be answered by using either statement alone.c)If the question can be answered by using both statements together, but cannot be answered by using either statement alone.d)If the question cannot be answered even by using both the statements togetherCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about There is a question statement which is followed by two statements A and B. You have to decide whether the information provided in the two statements is sufficient for answering the question.What is the sum of square of all the roots of the equation x4 + ax3 + cx2 +dx + e?(A) e = 89(B) All the roots are integers.a)If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.b)If the question can be answered by using either statement alone.c)If the question can be answered by using both statements together, but cannot be answered by using either statement alone.d)If the question cannot be answered even by using both the statements togetherCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There is a question statement which is followed by two statements A and B. You have to decide whether the information provided in the two statements is sufficient for answering the question.What is the sum of square of all the roots of the equation x4 + ax3 + cx2 +dx + e?(A) e = 89(B) All the roots are integers.a)If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.b)If the question can be answered by using either statement alone.c)If the question can be answered by using both statements together, but cannot be answered by using either statement alone.d)If the question cannot be answered even by using both the statements togetherCorrect answer is option 'C'. Can you explain this answer?.
There is a question statement which is followed by two statements A and B. You have to decide whether the information provided in the two statements is sufficient for answering the question.What is the sum of square of all the roots of the equation x4 + ax3 + cx2 +dx + e?(A) e = 89(B) All the roots are integers.a)If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.b)If the question can be answered by using either statement alone.c)If the question can be answered by using both statements together, but cannot be answered by using either statement alone.d)If the question cannot be answered even by using both the statements togetherCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about There is a question statement which is followed by two statements A and B. You have to decide whether the information provided in the two statements is sufficient for answering the question.What is the sum of square of all the roots of the equation x4 + ax3 + cx2 +dx + e?(A) e = 89(B) All the roots are integers.a)If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.b)If the question can be answered by using either statement alone.c)If the question can be answered by using both statements together, but cannot be answered by using either statement alone.d)If the question cannot be answered even by using both the statements togetherCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There is a question statement which is followed by two statements A and B. You have to decide whether the information provided in the two statements is sufficient for answering the question.What is the sum of square of all the roots of the equation x4 + ax3 + cx2 +dx + e?(A) e = 89(B) All the roots are integers.a)If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.b)If the question can be answered by using either statement alone.c)If the question can be answered by using both statements together, but cannot be answered by using either statement alone.d)If the question cannot be answered even by using both the statements togetherCorrect answer is option 'C'. Can you explain this answer?.
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