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Given the equation x2 + bx + c = 0, where b and c are constants, what is the value of c?
(1) The sum of the roots of the equation is zero.
(2) The sum of the squares of the roots of the equation is equal to 18.
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- d)EACH statement ALONE is sufficient.
- e)Statements (1) and (2) TOGETHER are NOT sufficient.
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Given the equation x2 + bx + c = 0, where b and c are constants, what ...
Steps 1 & 2: Understand Question and Draw Inferences
Given equation is
x2+bx+c=0 …………….. (I)
Let us suppose that the roots of this equation are p and q.
Given that b and c are constants, we need to find the value of c.
We know that for a quadratic equation
ax2+bx+c=0
Sum of roots = −b/a
Product of roots = c/a
In the given equation, a = 1
Therefore,
Sum of roots = -b
Product of roots = c
Step 3: Analyze Statement 1
It is given that the sum of roots of (I) is zero.
So, we have:
-b = p + q = 0
- b = 0 ………….. (II)
We cannot find the value of c from this information.
Statement 1 alone is not sufficient to arrive at a unique answer.
Step 4: Analyze Statement 2
Now let us look at statement 2.
Writing it in equation form, we have:
p2+q2=18
We know that
p2+q2=(p+q)2−2pq
- p2+q2=(−b)2−2c
- (−b)2−2c=18
- b2−2c=18 ………….. (III)
But we need the value of b here to find the value of c.
Statement 2 alone is not sufficient to arrive at a unique answer.
Step 5: Analyze Both Statements Together (if needed)
Now, let us look at both the statements together.
From statement 1, we have
b = 0
From statement 2, we have
b2 - 2c = 18
Combining both of these, we get:
-2c = 18
- c = -9
Answer: Option (C)
Most Upvoted Answer
Given the equation x2 + bx + c = 0, where b and c are constants, what ...
Solution:
Given equation is x2 bx c = 0, where b and c are constants
To find: value of c
Statement 1: The sum of the roots of the equation is zero.
Let the roots of the equation be α and β. Then, we know that:
α + β = −b
αβ = c
The sum of the roots is zero, so:
α + β = 0
−b = 0
b = 0
From the equation, we can conclude that c = αβ = 0. This statement alone is sufficient to answer the question.
Statement 2: The sum of the squares of the roots of the equation is equal to 18.
Let the roots of the equation be α and β. Then, we know that:
α + β = −b
αβ = c
We are given that:
α2 + β2 = 18
Squaring the equation α + β = −b, we get:
α2 + 2αβ + β2 = b2
Substituting the values of αβ and b2, we get:
α2 + 2c + β2 = b2
α2 + β2 = b2 − 2c
Substituting the given value of α2 + β2, we get:
18 = b2 − 2c
We can solve for c in terms of b:
c = (b2 − 18)/2
However, we do not know the value of b, so we cannot determine the value of c. This statement alone is not sufficient to answer the question.
Together, statements 1 and 2 give us:
b = 0
α2 + β2 = b2 − 2c = 0 − 2c = −2c
Substituting the given value of α2 + β2, we get:
18 = −2c
c = −9
Therefore, both statements together are sufficient to answer the question. The answer is (C).
Given equation is x2 bx c = 0, where b and c are constants
To find: value of c
Statement 1: The sum of the roots of the equation is zero.
Let the roots of the equation be α and β. Then, we know that:
α + β = −b
αβ = c
The sum of the roots is zero, so:
α + β = 0
−b = 0
b = 0
From the equation, we can conclude that c = αβ = 0. This statement alone is sufficient to answer the question.
Statement 2: The sum of the squares of the roots of the equation is equal to 18.
Let the roots of the equation be α and β. Then, we know that:
α + β = −b
αβ = c
We are given that:
α2 + β2 = 18
Squaring the equation α + β = −b, we get:
α2 + 2αβ + β2 = b2
Substituting the values of αβ and b2, we get:
α2 + 2c + β2 = b2
α2 + β2 = b2 − 2c
Substituting the given value of α2 + β2, we get:
18 = b2 − 2c
We can solve for c in terms of b:
c = (b2 − 18)/2
However, we do not know the value of b, so we cannot determine the value of c. This statement alone is not sufficient to answer the question.
Together, statements 1 and 2 give us:
b = 0
α2 + β2 = b2 − 2c = 0 − 2c = −2c
Substituting the given value of α2 + β2, we get:
18 = −2c
c = −9
Therefore, both statements together are sufficient to answer the question. The answer is (C).
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Given the equation x2 + bx + c = 0, where b and c are constants, what is the value of c?(1) The sum of the roots of the equation is zero.(2) The sum of the squares of the roots of the equation is equal to 18.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? for GMAT 2026 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Given the equation x2 + bx + c = 0, where b and c are constants, what is the value of c?(1) The sum of the roots of the equation is zero.(2) The sum of the squares of the roots of the equation is equal to 18.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given the equation x2 + bx + c = 0, where b and c are constants, what is the value of c?(1) The sum of the roots of the equation is zero.(2) The sum of the squares of the roots of the equation is equal to 18.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?.
Given the equation x2 + bx + c = 0, where b and c are constants, what is the value of c?(1) The sum of the roots of the equation is zero.(2) The sum of the squares of the roots of the equation is equal to 18.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? for GMAT 2026 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Given the equation x2 + bx + c = 0, where b and c are constants, what is the value of c?(1) The sum of the roots of the equation is zero.(2) The sum of the squares of the roots of the equation is equal to 18.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given the equation x2 + bx + c = 0, where b and c are constants, what is the value of c?(1) The sum of the roots of the equation is zero.(2) The sum of the squares of the roots of the equation is equal to 18.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?.
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