What are the roots of the quadratic equation x2 + bx + c = 0 if the roots are distinct and at equal distance from 5 on the number line?(1)The product of the roots of the equation x2 + bx + c = 0 is 21(2) x 7 is a factor of the expression 7x2 + 7bx + 7ca)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?

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What are the roots of the quadratic equation x² + bx + c = 0 if the roots are distinct and at equal distance from 5 on the number line?

(1) The product of the roots of the equation x² + bx + c = 0 is 21

(2) x – 7 is a factor of the expression 7x² + 7bx + 7c

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Correct answer is option 'D'. Can you explain this answer?

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What are the roots of the quadratic equation x2 + bx + c = 0 if the ro...

Steps 1 & 2: Understand Question and Draw Inferences

x²+bx+c=0

Let the distance of the roots of the equation from 5 be d.
- So, the roots will be 5 +d and 5 – d
  - Since the 2 roots are distinct, d ≠ 0
- The sum of the roots = (5+d) + (5-d) = 10
  - So, −b/a=10
  - In the given quadratic equation, a, which denotes the coefficient of x², is 1.
  - So b = -10

To Find: As we have assumed the roots of the equation to be (5 +d) and (5 –d), to find the roots, we need to find the value of d

Step 3: Analyze Statement 1 independently

(1) The product of the roots of the equation x² + bx + c = 0 is 21

Product of roots = c/a=21

Since a = 1 in this equation, we can infer that c = 21
We need to find the roots of x²−10x+21=0

Since, we know the quadratic equation, we can find the roots of the equation.

Sufficient to answer

Alternate Method:

Product of roots = (5+d) (5-d) = 21
5²−d²=21

d² = 25 - 21 = 4
d = 2 or -2
For d = 2
- Roots = 5+2 = 7 and 5-2 = 3
For d = -2
- Roots = 5-2 = 3 and 5+2 = 7

So, the roots of the equation are 3 and 7

Sufficient to answer

Step 4: Analyze Statement 2 independently

(2) x – 7 is a factor of the expression 7x² + 7bx + 7c

x- 7 is a factor of the expression 7(x²+bx+c)

Since 7 is a constant

(x-7) is a factor of the expression x2+bx+c

Therefore,

x = 7 is one of the roots of the equation x2+bx+c=0

That is

5 + d = 7,
- So, d = 2 and hence the other root is 5 – d = 3. OR
5 – d = 7
- So, d = -2 and hence the other root is 5 +(-2) = 3

In both the cases, we get the same values of the roots.

Sufficient to answer

Step 5: Analyze Both Statements Together (if needed)

As we have a unique answer from steps 3 and 4, this step is not required

Answer: D

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What are the roots of the quadratic equation x2 + bx + c = 0 if the roots are distinct and at equal distance from 5 on the number line?(1)The product of the roots of the equation x2 + bx + c = 0 is 21(2) x – 7 is a factor of the expression 7x2 + 7bx + 7ca)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?

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What are the roots of the quadratic equation x2 + bx + c = 0 if the roots are distinct and at equal distance from 5 on the number line?(1)The product of the roots of the equation x2 + bx + c = 0 is 21(2) x – 7 is a factor of the expression 7x2 + 7bx + 7ca)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What are the roots of the quadratic equation x2 + bx + c = 0 if the roots are distinct and at equal distance from 5 on the number line?(1)The product of the roots of the equation x2 + bx + c = 0 is 21(2) x – 7 is a factor of the expression 7x2 + 7bx + 7ca)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What are the roots of the quadratic equation x2 + bx + c = 0 if the roots are distinct and at equal distance from 5 on the number line?(1)The product of the roots of the equation x2 + bx + c = 0 is 21(2) x – 7 is a factor of the expression 7x2 + 7bx + 7ca)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?.

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