XAT Quadratic Equations questions

XAT 2024 Quadratic Equations questions

Question 1

The roots of the polynomial $$P(x) = 2x^3 - 11x^2 + 17x - 6$$ are the radii of three concentric circles.
The ratio of their area, when arranged from the largest to the smallest, is:

XAT 2022 Quadratic Equations questions

Question 1

Some members of a social service organization in Kolkata decide to prepare 2400 laddoos to gift to children in various orphanages and slums in the city, during Durga puja. The plan is that each of them makes the same number of laddoos. However, on the laddoo-making day, ten members are absent, thus each remaining member makes 12  laddoos more than earlier decided.

How many members actually make the laddoos?

Question 2

The sum of the cubes of two numbers is 128, while the sum of the reciprocals of their cubes is 2.

What is the product of the squares of the numbers?

XAT 2021 Quadratic Equations questions

Question 1

Let $$f(x) = \frac{x^2 + 1}{x^2 - 1}$$ if $$x \neq 1, -1,$$ and 1 if x = 1, -1. Let $$g(x) = \frac{x + 1}{x - 1}$$ if $$x \neq 1,$$ and 3 if x = 1.
What is the minimum possible values of $$\frac{f(x)}{g(x)}$$ ?

XAT 2019 Quadratic Equations questions

Question 1

Given that a and b are integers and that $$5x+2\sqrt{7}$$ is a root of the polynomial $$x^2 - ax + b + 2\sqrt{7}$$ in $$x$$, what is the value of b?

Question 2

If $$x^2 + x + 1 = 0$$, then $$x^{2018} + x^{2019}$$ equals which of the following:

XAT 2018 Quadratic Equations questions

Question 1

Two different quadratic equations have a common root. Let the three unique roots of the two equations be A, B and C - all of them are positive integers. If (A + B + C) = 41 and the product of the roots of one of the equations is 35, which of the following options is definitely correct?

XAT 2013 Quadratic Equations questions

Question 1

Consider a function $$f(x) = x^4 + x^3 + x^2 + x + 1$$, where x is a positive integer greater than 1. What will be the remainder if $$f(x^5)$$ is divided by f(x)?