# Top 35 CAT Quadratic Equations Questions With Solutions

## CAT Quadratic Equations Questions Weightage Over Past 5 Years

 Year Weightage 2022 5 2021 6 2020 4 2019 4 2018 2

## CAT Quadratic Equations Formulas PDF

Quadratic equations are an essential topic in the quantitative aptitude section, and it is vital to have a clear understanding of the formulas related to it. To help the aspirants to ace this topic, we have made a PDF containing a comprehensive list of formulas, tips, and tricks that you can use to solve quadratic equation problems with ease and speed. Click on the below link to download CAT Quadratic Equations Formulas PDF.

## CAT 2022 Quadratic Equations questions

#### Question 1

Suppose k is any integer such that the equation $$2x^{2}+kx+5=0$$ has no real roots and the equation $$x^{2}+(k-5)x+1=0$$ has two distinct real roots for x. Then, the number of possible values of k is

#### Question 2

If $$(3+2\sqrt{2})$$ is a root of the equation $$ax^{2}+bx+c=0$$ and $$(4+2\sqrt{3})$$ is a root of the equation $$ay^{2}+my+n=0$$ where a, b, c, m and n are integers, then the value of $$(\frac{b}{m}+\frac{c-2b}{n})$$ is

#### Question 3

Let r and c be real numbers. If r and -r are roots of $$5x^{3} + cx^{2} - 10x + 9 = 0$$, then c equals

#### Question 4

Let a, b, c be non-zero real numbers such that $$b^2 < 4ac$$, and $$f(x) = ax^2 + bx + c$$. If the set S consists of all integers m such that f(m) < 0, then the set S must necessarily be

#### Question 5

The minimum possible value of $$\frac{x^{2} - 6x + 10}{3-x}$$, for $$x < 3$$, is

## CAT 2021 Quadratic Equations questions

#### Question 1

A shop owner bought a total of 64 shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was INR 50 less than that of a large shirt. She paid a total of INR 5000 for the large shirts, and a total of INR 1800 for the small shirts. Then, the price of a large shirt and a small shirt together, in INR, is

#### Question 2

Suppose one of the roots of the equation $$ax^{2}-bx+c=0$$ is $$2+\sqrt{3}$$, Where a,b and c are rational numbers and $$a\neq0$$. If $$b=c^{3}$$ then $$\mid a\mid$$ equals.

#### Question 3

For all real values of x, the range of the function $$f(x)=\frac{x^{2}+2x+4}{2x^{2}+4x+9}$$ is:

#### Question 4

Suppose hospital A admitted 21 less Covid infected patients than hospital B, and all eventually recovered. The sum of recovery days for patients in hospitals A and B were 200 and 152, respectively. If the average recovery days for patients admitted in hospital A was 3 more than the average in hospital B then the number admitted in hospital A was

#### Question 5

Consider the pair of equations: $$x^{2}-xy-x=22$$ and $$y^{2}-xy+y=34$$. If $$x>y$$, then $$x-y$$ equals

#### Question 6

If r is a constant such that $$\mid x^2 - 4x - 13 \mid = r$$ has exactly three distinct real roots, then the value of r is

## CAT 2020 Quadratic Equations questions

#### Question 1

Let m and n be positive integers, If $$x^{2}+mx+2n=0$$ and $$x^{2}+2nx+m=0$$ have real roots, then the smallest possible value of $$m+n$$ is

#### Question 2

How many disticnt positive integer-valued solutions exist to the equation $$(x^{2}-7x+11)^{(x^{2}-13x+42)}=1$$ ?

#### Question 3

The number of distinct real roots of the equation $$(x+\frac{1}{x})^{2}-3(x+\frac{1}{x})+2=0$$ equals

#### Question 4

The number of integers that satisfy the equality $$(x^{2}-5x+7)^{x+1}=1$$ is

## CAT 2019 Quadratic Equations questions

#### Question 1

The product of the distinct roots of $$\mid x^2 - x - 6 \mid = x + 2$$ is

#### Question 2

Let A be a real number. Then the roots of the equation $$x^2 - 4x - log_{2}{A} = 0$$ are real and distinct if and only if

#### Question 3

The quadratic equation $$x^2 + bx + c = 0$$ has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of $$b^2 + c$$?

#### Question 4

The number of solutions to the equation $$\mid x \mid (6x^2 + 1) = 5x^2$$ is

## CAT 2018 Quadratic Equations questions

#### Question 1

If $$U^{2}+(U-2V-1)^{2}$$= −$$4V(U+V)$$ , then what is the value of $$U+3V$$ ?

#### Question 2

If a and b are integers such that $$2x^2−ax+2>0$$ and $$x^2−bx+8≥0$$ for all real numbers $$x$$, then the largest possible value of $$2a−6b$$ is

## CAT 2017 Quadratic Equations questions

#### Question 1

If $$x+1=x^{2}$$ and $$x>0$$, then $$2x^{4}$$  is

## CAT 2008 Quadratic Equations questions

#### Question 1

If the roots of the equation $$x^3 - ax^2 + bx - c = 0$$ are three consecutive integers, then what is the smallest possible value of b?

[CAT 2008]

## CAT 2007 Quadratic Equations questions

#### Question 1

A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f (x) at x = 10?

## CAT 2005 Quadratic Equations questions

#### Question 1

For which value of k does the following pair of equations yield a unique solution for x such that the solution is positive?

$$x^2 - y^2 = 0$$

$$(x-k)^2 + y^2 = 1$$

## CAT 2003 Quadratic Equations questions

#### Question 1

Let p and q be the roots of the quadratic equation $$x^2 - (\alpha - 2) x - \alpha -1= 0$$ . What is the minimum possible value of $$p^2 + q^2$$?

## CAT 2002 Quadratic Equations questions

#### Question 1

The number of real roots of the equation $$A^2/x + B^2/(x-1) = 1$$ , where A and B are real numbers not equal to zero simultaneously, is

#### Question 2

Davji Shop sells samosas in boxes of different sizes. The samosas are priced at Rs. 2 per samosa up to 200 samosas. For every additional 20 samosas, the price of the whole lot goes down by 10 paise per samosa. What should be the maximum size of the box that would maximise the revenue?

## CAT 2001 Quadratic Equations questions

#### Question 1

Ujakar and Keshab attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4, 3). Keshab made a mistake in writing down the coefficient of x. He got the roots as (3, 2). What will be the exact roots of the original quadratic equation?

## CAT 2000 Quadratic Equations questions

#### Question 1

If the equation $$x^3 - ax^2 + bx - a = 0$$ has three real roots, then it must be the case that,

## CAT 1997 Quadratic Equations questions

#### Question 1

If the roots $$x_1$$ and $$x_2$$ are the roots of the quadratic equation $$x^2 -2x+c=0$$ also satisfy the equation $$7x_2 - 4x_1 = 47$$, then which of the following is true?

## CAT 1996 Quadratic Equations questions

#### Question 1

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?

## CAT 1990 Quadratic Equations questions

#### Question 1

The value of $$\frac{(1-d^3)}{(1-d)}$$ is

#### Question 2

The roots of the equation $$ax^{2} + 3x + 6 = 0$$ will be reciprocal to each other if the value of a is

#### Question 3

If $$xy + yz + zx = 0$$, then $$(x + y + z)^2$$ equals