Question:
Ujakar and Keshab attempted to solve a quadratic equation.
- Ujakar made a mistake in writing down the constant term and got roots (4, 3).
- Keshab made a mistake in writing down the coefficient of $x$ and got roots (3, 2).
What will be the exact roots of the original quadratic equation?
Ujakar and Keshab attempted to solve a quadratic equation.
- Ujakar made a mistake in writing down the constant term and got roots (4, 3).
- Keshab made a mistake in writing down the coefficient of $x$ and got roots (3, 2).
What will be the exact roots of the original quadratic equation?
- Ujakar made a mistake in writing down the constant term and got roots (4, 3).
- Keshab made a mistake in writing down the coefficient of $x$ and got roots (3, 2).
What will be the exact roots of the original quadratic equation?
Show Hint
When two people make different mistakes, compare the correct parts of each to reconstruct the true equation.
Updated On: Mar 20, 2026
- (6, 1)
- ($-3, -4$)
- (4, 3)
- ($-4, -3$)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Let original quadratic be $x^2 + px + q = 0$.
From Ujakar’s roots (4, 3): sum $= 7 \Rightarrow p = -7$, product $= 12 \Rightarrow$ wrong constant $q' = 12$.
From Keshab’s roots (3, 2): sum $= 5 \Rightarrow p' = -5$ (wrong coefficient), product $= 6 \Rightarrow$ correct constant $q = 6$.
So actual: $x^2 - 7x + 6 = 0$, roots = 6 and 1.
From Ujakar’s roots (4, 3): sum $= 7 \Rightarrow p = -7$, product $= 12 \Rightarrow$ wrong constant $q' = 12$.
From Keshab’s roots (3, 2): sum $= 5 \Rightarrow p' = -5$ (wrong coefficient), product $= 6 \Rightarrow$ correct constant $q = 6$.
So actual: $x^2 - 7x + 6 = 0$, roots = 6 and 1.
Was this answer helpful?
0
0
Top CAT Quantitative Aptitude Questions
- In a triangle ABC,AB=AC=8cm. A circle drawn with BC as diameter passes through A. Another circle drawn with center at A passes through B and C. Then the area,in sq.cm,of the overlapping region between the two circles is
- The simple interest accrued on an amount of Rs.25,000 at the end of three years is Rs.7,500. What would be the compound interest accrued on the same amount at the same rate in the same period?
- What is the sum of all roots of the equation \(|x+4|^2–10|x+4|=24\)?
- A solid metal sphere is melted and smaller spheres of equal radii are formed. 10% of the volume of the sphere is lost in the process. The smaller spheres have a radius which is \(\frac{1}{9}\text{th}\) the larger sphere. If 10 litres of paint were needed to paint the larger sphere,how many litres are needed to paint all the smaller spheres?
- The ratio of the ages of a husband and his wife when they got married was 6:5. 4 years and 6 years after their marriage they had their 1st and 2nd children. The sum of the present ages of the husband and wife is 6.4 times the sum of the present ages of their children. The average age of the family at present is 18.5 years. Find the ratio of the ages of the husband and wife when their second child was born.
View More Questions
Top CAT Quadratic Equations Questions
For what value of \( k \) does the following pair of equations yield a unique solution for \( x \), such that the solution is positive?
\(x^2 - 3y^2 = 0 \)
\(x^2 - 6y^2 + k = 0 \)- What is the other root of \(f(x) = 0\)?
- What is the value of \(a + b + c\) given the above conditions?
- Given the quadratic equation $x^2 - (A - 3)x - (A - 2)$, for what value of A will the sum of the squares of the roots be zero?
- If x2 − 5x + 6 = 0, what is the sum of the roots?
View More Questions
Top CAT Questions
- Compare and contrast between Portia and Jessica characters in Merchant of Venice.
- In a triangle ABC,AB=AC=8cm. A circle drawn with BC as diameter passes through A. Another circle drawn with center at A passes through B and C. Then the area,in sq.cm,of the overlapping region between the two circles is
- The simple interest accrued on an amount of Rs.25,000 at the end of three years is Rs.7,500. What would be the compound interest accrued on the same amount at the same rate in the same period?
- What is the sum of all roots of the equation \(|x+4|^2–10|x+4|=24\)?
- A solid metal sphere is melted and smaller spheres of equal radii are formed. 10% of the volume of the sphere is lost in the process. The smaller spheres have a radius which is \(\frac{1}{9}\text{th}\) the larger sphere. If 10 litres of paint were needed to paint the larger sphere,how many litres are needed to paint all the smaller spheres?
View More Questions