Ram and Shyam attempted to solve a quadratic ...
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)
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

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).

The exact roots of the original quadratic equation are (3, 2), which is option A.
Related Test
 CAT Practice Test - 33100 Ques | 180 Mins
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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