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If x2+4x+p=13 , where p is a constant, what is the product of the roots of this quadratic equation?
(1) -2 is one of the roots of the quadratic equation
(2) x2+4x+p=13 has equal roots
- 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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Verified Answer
If x2+4x+p=13 , where p is a constant, what is the product of the root...
Step 1 & Step 2: Understanding the Question statement and Drawing Inferences
Given Info:
- x2+4x+p=13
- Rewriting the above quadratic equation in standard form ax2+bx+c=0
- Subtracting 13 from both sides, we have
⇒ x2+4x+p−13=13−13
⇒ x2+4x+p−13=0
To find:
- We need to find the product of the quadratic equation → x2+4x+p−13=0
- To find the product of the roots:
- We need to know the roots or
- Products of roots of the quadratic equation ax2+bx+c=0 , is given by c/a
- So product of roots of the above quadratic equation will be (p−13)/1 , as →c=p-13 and a=1
- Now since we do not know the value of p-13, we will not be able to determine the product of roots of the quadratic equation.
- Thus we need to analyse the given statements further to determine the value of p, to be able to calculate the product of roots of the quadratic equation.
Step 3: Analyze statement 1 independently
Statement 1:
- -2 is one of the roots of the quadratic equation
- So, -2 will satisfy the given quadratic equation → x2+4x+p−13=0
⇒ (-2)2 + 4(-2) + p - 13 = 0
⇒ 4 - 8 + p - 13 = 0
⇒ p = 17
- Now since we know the value of p, we will be able to find the value of p-13 and thus will be able to calculate the value of product of quadratic equation.
- Hence statement 1 is sufficient to answer the question.
Step 4: Analyze statement 2 independently
Statement 2:
- Quadratic equation has equal roots
- For equal roots, we will use the relation of sum of roots of the quadratic equation to determine the value of the equal root.
- Sum of roots of the quadratic equation ax2+bx+c=0 , is −b/a
- So sum of roots of the quadratic equation → x2+4x+p−13=0 will be −4/1 , where b=4 and a=1
- Now since both roots are equal and the sum of the roots is coming as -4, both roots will thus be equal to – 2 each.
- Now, the equal root → -2, will satisfy the given quadratic equation x2+4x+p−13=0
⇒(-2)2 + 4(-2) + p - 13 = 0
⇒ p=17
- Now since we know the value of p, we will be able to find the value of p-13 and thus will be able to calculate the value of product of quadratic equation.
- Hence statement 2 is sufficient to answer the question
Step 5: Analyze the two statements together
- Since from statement 1 and statement 2, we are able to arrive at a unique answer, combining and analysing statements together is not required.
Hence the correct answer is option D
Most Upvoted Answer
If x2+4x+p=13 , where p is a constant, what is the product of the root...
Statement (1): -2 is one of the roots of the quadratic equation
Let's assume the quadratic equation is in the form ax^2 + bx + c = 0.
From the given information, we know that one of the roots is -2. This means that when x = -2, the quadratic equation is satisfied. Plugging this value into the equation, we get:
(-2)^2 + 4(-2) + p = 13
4 - 8 + p = 13
-4 + p = 13
p = 17
Statement (2): x^2 + 4x + p = 13 has equal roots
This means that the discriminant of the quadratic equation is zero. The discriminant is given by b^2 - 4ac.
In this case, a = 1, b = 4, and c = p - 13.
So, the discriminant is:
(4)^2 - 4(1)(p - 13) = 0
16 - 4p + 52 = 0
-4p + 68 = 0
-4p = -68
p = 17
Combined solution:
From both statements, we have determined that p = 17. Therefore, we can find the roots of the quadratic equation:
x^2 + 4x + 17 = 0
Using the quadratic formula, the roots can be calculated as follows:
x = (-b ± √(b^2 - 4ac)) / (2a)
x = (-4 ± √(4^2 - 4(1)(17))) / (2(1))
x = (-4 ± √(16 - 68)) / 2
x = (-4 ± √(-52)) / 2
Since the discriminant is negative, the roots are imaginary and the product of the roots will also be imaginary. Therefore, the product of the roots cannot be determined based on the given information.
Answer:
Neither statement alone nor both statements together are sufficient to answer the question asked.
Let's assume the quadratic equation is in the form ax^2 + bx + c = 0.
From the given information, we know that one of the roots is -2. This means that when x = -2, the quadratic equation is satisfied. Plugging this value into the equation, we get:
(-2)^2 + 4(-2) + p = 13
4 - 8 + p = 13
-4 + p = 13
p = 17
Statement (2): x^2 + 4x + p = 13 has equal roots
This means that the discriminant of the quadratic equation is zero. The discriminant is given by b^2 - 4ac.
In this case, a = 1, b = 4, and c = p - 13.
So, the discriminant is:
(4)^2 - 4(1)(p - 13) = 0
16 - 4p + 52 = 0
-4p + 68 = 0
-4p = -68
p = 17
Combined solution:
From both statements, we have determined that p = 17. Therefore, we can find the roots of the quadratic equation:
x^2 + 4x + 17 = 0
Using the quadratic formula, the roots can be calculated as follows:
x = (-b ± √(b^2 - 4ac)) / (2a)
x = (-4 ± √(4^2 - 4(1)(17))) / (2(1))
x = (-4 ± √(16 - 68)) / 2
x = (-4 ± √(-52)) / 2
Since the discriminant is negative, the roots are imaginary and the product of the roots will also be imaginary. Therefore, the product of the roots cannot be determined based on the given information.
Answer:
Neither statement alone nor both statements together are sufficient to answer the question asked.
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If x2+4x+p=13 , where p is a constant, what is the product of the roots of this quadratic equation?(1) -2 is one of the roots of the quadratic equation(2) x2+4x+p=13 has equal rootsa)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?
Question Description
If x2+4x+p=13 , where p is a constant, what is the product of the roots of this quadratic equation?(1) -2 is one of the roots of the quadratic equation(2) x2+4x+p=13 has equal rootsa)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 If x2+4x+p=13 , where p is a constant, what is the product of the roots of this quadratic equation?(1) -2 is one of the roots of the quadratic equation(2) x2+4x+p=13 has equal rootsa)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 If x2+4x+p=13 , where p is a constant, what is the product of the roots of this quadratic equation?(1) -2 is one of the roots of the quadratic equation(2) x2+4x+p=13 has equal rootsa)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?.
If x2+4x+p=13 , where p is a constant, what is the product of the roots of this quadratic equation?(1) -2 is one of the roots of the quadratic equation(2) x2+4x+p=13 has equal rootsa)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 If x2+4x+p=13 , where p is a constant, what is the product of the roots of this quadratic equation?(1) -2 is one of the roots of the quadratic equation(2) x2+4x+p=13 has equal rootsa)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 If x2+4x+p=13 , where p is a constant, what is the product of the roots of this quadratic equation?(1) -2 is one of the roots of the quadratic equation(2) x2+4x+p=13 has equal rootsa)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?.
Solutions for If x2+4x+p=13 , where p is a constant, what is the product of the roots of this quadratic equation?(1) -2 is one of the roots of the quadratic equation(2) x2+4x+p=13 has equal rootsa)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? in English & in Hindi are available as part of our courses for GMAT.
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ample number of questions to practice If x2+4x+p=13 , where p is a constant, what is the product of the roots of this quadratic equation?(1) -2 is one of the roots of the quadratic equation(2) x2+4x+p=13 has equal rootsa)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? tests, examples and also practice GMAT tests.
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