CAT Question > Ram and Shyam attempted to solve a quadratic ...
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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?
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
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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.
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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).
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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?
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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 2023 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 2023 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 2023 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 2023 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.
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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
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