CAT Exam > CAT Questions > Ram and Shyam attempted to solve a quadratic ...
Start Learning for Free
Ram and Shyam attempted to solve a quadratic equation. Ram made a mistake in writing down the constant term. He ended up with the roots (4, 3). Shyam made a mistake in writing down the coefficient of x. He got the root as (3, 2). What will be the exact roots of the original quadratic equation?
- a)(6, 1)
- b)(-3, -4)
- c)(4, 3)
- d)(-4, -3)
- e)(-4, 3)
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Ram and Shyam attempted to solve a quadratic equation. Ram made a mist...
ax2 + bx + c
Sum of roots : -b/a => 7
Product = c/a => 6
x2 - (sum of roots)x + Product
x2 - 7x + 6 = 0
x2 - 6x - x + 6 = 0
x(x-6) -1(x-6) = 0
(x-1)(x-6) = 0
x = 1,6
Sum of roots : -b/a => 7
Product = c/a => 6
x2 - (sum of roots)x + Product
x2 - 7x + 6 = 0
x2 - 6x - x + 6 = 0
x(x-6) -1(x-6) = 0
(x-1)(x-6) = 0
x = 1,6
Most Upvoted Answer
Ram and Shyam attempted to solve a quadratic equation. Ram made a mist...
Given information:
- Ram's mistake: Constant term is wrong
- Shyam's mistake: Coefficient of x is wrong
- Ram's roots: (4, 3)
- Shyam's root: (3, 2)
Approach:
We know that for a quadratic equation of the form ax^2 + bx + c = 0, the sum of roots is -b/a and the product of roots is c/a. Using this information, we can solve for the correct coefficients of the quadratic equation.
Solution:
Let's first solve for the correct constant term using Ram's roots:
- Sum of roots = -b/a = 4 + 3 = 7
- Product of roots = c/a = 4 * 3 = 12
- We know that the quadratic equation with roots (p, q) is of the form (x - p)(x - q) = 0. Using this, we can write the equation with roots (4, 3) as:
(x - 4)(x - 3) = 0
x^2 - 7x + 12 = 0
- Therefore, the correct constant term is 12.
Now, let's solve for the correct coefficient of x using Shyam's root:
- Using the correct constant term of 12, we can write the quadratic equation as:
x^2 - bx + 12 = 0
- Shyam's root is (3, 2), so we know that the two roots of the quadratic equation are 3 and 2.
- Using the sum of roots, we get:
3 + 2 = b/1
b = 5
- Therefore, the correct quadratic equation is:
x^2 - 5x + 12 = 0
- Solving for the roots using the quadratic formula, we get:
x = (5 ± sqrt(25 - 4*12))/2
x = (5 ± 1)/2
x = 3 or x = 2/1
- Therefore, the exact roots of the original quadratic equation are (3, 2).
Answer:
The exact roots of the original quadratic equation are (3, 2), which is option A.
- Ram's mistake: Constant term is wrong
- Shyam's mistake: Coefficient of x is wrong
- Ram's roots: (4, 3)
- Shyam's root: (3, 2)
Approach:
We know that for a quadratic equation of the form ax^2 + bx + c = 0, the sum of roots is -b/a and the product of roots is c/a. Using this information, we can solve for the correct coefficients of the quadratic equation.
Solution:
Let's first solve for the correct constant term using Ram's roots:
- Sum of roots = -b/a = 4 + 3 = 7
- Product of roots = c/a = 4 * 3 = 12
- We know that the quadratic equation with roots (p, q) is of the form (x - p)(x - q) = 0. Using this, we can write the equation with roots (4, 3) as:
(x - 4)(x - 3) = 0
x^2 - 7x + 12 = 0
- Therefore, the correct constant term is 12.
Now, let's solve for the correct coefficient of x using Shyam's root:
- Using the correct constant term of 12, we can write the quadratic equation as:
x^2 - bx + 12 = 0
- Shyam's root is (3, 2), so we know that the two roots of the quadratic equation are 3 and 2.
- Using the sum of roots, we get:
3 + 2 = b/1
b = 5
- Therefore, the correct quadratic equation is:
x^2 - 5x + 12 = 0
- Solving for the roots using the quadratic formula, we get:
x = (5 ± sqrt(25 - 4*12))/2
x = (5 ± 1)/2
x = 3 or x = 2/1
- Therefore, the exact roots of the original quadratic equation are (3, 2).
Answer:
The exact roots of the original quadratic equation are (3, 2), which is option A.
Free Test
FREE
| Start Free Test |
Community Answer
Ram and Shyam attempted to solve a quadratic equation. Ram made a mist...
RAM considered the equation as x^2 - 7x +12 and SHYAM considered the equation as x^2 -5x+6. Since Ram and Shyam made mistakes in constant term and coefficient of x term respectively so the correct(original) equation will be x^2 -7x +6 and the corresponding roots of this equation will be (6,1).
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
Ram and Shyam attempted to solve a quadratic equation. Ram made a mistake in writing down the constant term. He ended up with the roots (4, 3). Shyam made a mistake in writing down the coefficient ofx. He got the root as (3, 2). What will be the exact roots of the original quadratic equation?a)(6, 1)b)(-3, -4)c)(4, 3)d)(-4, -3)e)(-4, 3)Correct answer is option 'A'. Can you explain this answer?
Question Description
Ram and Shyam attempted to solve a quadratic equation. Ram made a mistake in writing down the constant term. He ended up with the roots (4, 3). Shyam made a mistake in writing down the coefficient ofx. He got the root as (3, 2). What will be the exact roots of the original quadratic equation?a)(6, 1)b)(-3, -4)c)(4, 3)d)(-4, -3)e)(-4, 3)Correct answer is option 'A'. 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 Ram and Shyam attempted to solve a quadratic equation. Ram made a mistake in writing down the constant term. He ended up with the roots (4, 3). Shyam made a mistake in writing down the coefficient ofx. He got the root as (3, 2). What will be the exact roots of the original quadratic equation?a)(6, 1)b)(-3, -4)c)(4, 3)d)(-4, -3)e)(-4, 3)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ram and Shyam attempted to solve a quadratic equation. Ram made a mistake in writing down the constant term. He ended up with the roots (4, 3). Shyam made a mistake in writing down the coefficient ofx. He got the root as (3, 2). What will be the exact roots of the original quadratic equation?a)(6, 1)b)(-3, -4)c)(4, 3)d)(-4, -3)e)(-4, 3)Correct answer is option 'A'. Can you explain this answer?.
Ram and Shyam attempted to solve a quadratic equation. Ram made a mistake in writing down the constant term. He ended up with the roots (4, 3). Shyam made a mistake in writing down the coefficient ofx. He got the root as (3, 2). What will be the exact roots of the original quadratic equation?a)(6, 1)b)(-3, -4)c)(4, 3)d)(-4, -3)e)(-4, 3)Correct answer is option 'A'. 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 Ram and Shyam attempted to solve a quadratic equation. Ram made a mistake in writing down the constant term. He ended up with the roots (4, 3). Shyam made a mistake in writing down the coefficient ofx. He got the root as (3, 2). What will be the exact roots of the original quadratic equation?a)(6, 1)b)(-3, -4)c)(4, 3)d)(-4, -3)e)(-4, 3)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ram and Shyam attempted to solve a quadratic equation. Ram made a mistake in writing down the constant term. He ended up with the roots (4, 3). Shyam made a mistake in writing down the coefficient ofx. He got the root as (3, 2). What will be the exact roots of the original quadratic equation?a)(6, 1)b)(-3, -4)c)(4, 3)d)(-4, -3)e)(-4, 3)Correct answer is option 'A'. Can you explain this answer?.
Solutions for Ram and Shyam attempted to solve a quadratic equation. Ram made a mistake in writing down the constant term. He ended up with the roots (4, 3). Shyam made a mistake in writing down the coefficient ofx. He got the root as (3, 2). What will be the exact roots of the original quadratic equation?a)(6, 1)b)(-3, -4)c)(4, 3)d)(-4, -3)e)(-4, 3)Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of Ram and Shyam attempted to solve a quadratic equation. Ram made a mistake in writing down the constant term. He ended up with the roots (4, 3). Shyam made a mistake in writing down the coefficient ofx. He got the root as (3, 2). What will be the exact roots of the original quadratic equation?a)(6, 1)b)(-3, -4)c)(4, 3)d)(-4, -3)e)(-4, 3)Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Ram and Shyam attempted to solve a quadratic equation. Ram made a mistake in writing down the constant term. He ended up with the roots (4, 3). Shyam made a mistake in writing down the coefficient ofx. He got the root as (3, 2). What will be the exact roots of the original quadratic equation?a)(6, 1)b)(-3, -4)c)(4, 3)d)(-4, -3)e)(-4, 3)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Ram and Shyam attempted to solve a quadratic equation. Ram made a mistake in writing down the constant term. He ended up with the roots (4, 3). Shyam made a mistake in writing down the coefficient ofx. He got the root as (3, 2). What will be the exact roots of the original quadratic equation?a)(6, 1)b)(-3, -4)c)(4, 3)d)(-4, -3)e)(-4, 3)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Ram and Shyam attempted to solve a quadratic equation. Ram made a mistake in writing down the constant term. He ended up with the roots (4, 3). Shyam made a mistake in writing down the coefficient ofx. He got the root as (3, 2). What will be the exact roots of the original quadratic equation?a)(6, 1)b)(-3, -4)c)(4, 3)d)(-4, -3)e)(-4, 3)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Ram and Shyam attempted to solve a quadratic equation. Ram made a mistake in writing down the constant term. He ended up with the roots (4, 3). Shyam made a mistake in writing down the coefficient ofx. He got the root as (3, 2). What will be the exact roots of the original quadratic equation?a)(6, 1)b)(-3, -4)c)(4, 3)d)(-4, -3)e)(-4, 3)Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup