Quadratic equations questions come under the algebra concept in the quantitative section of CAT. The weightage for quadratic equations questions is lower. But these questions will help you boost your score in quant. It is advised to solve the questions that previously appeared in the CAT. To help the aspirants find the quadratic equations questions, we have compiled all the questions that appeared in the previous CAT papers and detailed video solutions explained by CAT experts. One can also download the PDF that contains all these questions with video solutions. And the best part is you can download the PDF for free without signing up.
Year | Weightage |
2022 | 5 |
2021 | 6 |
2020 | 4 |
2019 | 4 |
2018 | 2 |
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.
The sum of all possible values of x satisfying the equation $$2^{4x^{2}}-2^{2x^{2}+x+16}+2^{2x+30}=0$$, is
correct answer:-4
The equation $$x^{3} + (2r + 1)x^{2} + (4r - 1)x + 2 =0$$ has -2 as one of the roots. If the other two roots are real, then the minimum possible non-negative integer value of r is
correct answer:-2
A quadratic equation $$x^2 + bx + c = 0$$ has two real roots. If the difference between the reciprocals of the roots is $$\frac{1}{3}$$, and the sum of the reciprocals of the squares of the roots is $$\frac{5}{9}$$, then the largest possible value of $$(b + c)$$ is
correct answer:-9
Let $$\alpha$$ and $$\beta$$ be the two distinct roots of the equation $$2x^{2} - 6x + k = 0$$, such that ( $$\alpha + \beta$$) and $$\alpha \beta$$ are the distinct roots of the equation $$x^{2} + px + p = 0$$. Then, the value of 8(k - p) is
correct answer:-6
Let k be the largest integer such that the equation $$(x-1)^{2}+2kx+11=0$$ has no real roots. If y is a positive real number, then the least possible value of $$\frac{k}{4y}+9y$$ is
correct answer:-6
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
correct answer:-1
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
correct answer:-4
Let r and c be real numbers. If r and -r are roots of $$5x^{3} + cx^{2} - 10x + 9 = 0$$, then c equals
correct answer:-1
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
correct answer:-3
The minimum possible value of $$\frac{x^{2} - 6x + 10}{3-x}$$, for $$x < 3$$, is
correct answer:-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.
correct answer:-2
For all real values of x, the range of the function $$f(x)=\frac{x^{2}+2x+4}{2x^{2}+4x+9}$$ is:
correct answer:-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
correct answer:-35
Consider the pair of equations: $$x^{2}-xy-x=22$$ and $$y^{2}-xy+y=34$$. If $$x>y$$, then $$x-y$$ equals
correct answer:-4
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
correct answer:-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
correct answer:-2
How many disticnt positive integer-valued solutions exist to the equation $$(x^{2}-7x+11)^{(x^{2}-13x+42)}=1$$ ?
correct answer:-4
The number of distinct real roots of the equation $$(x+\frac{1}{x})^{2}-3(x+\frac{1}{x})+2=0$$ equals
correct answer:-1
The number of integers that satisfy the equality $$(x^{2}-5x+7)^{x+1}=1$$ is
correct answer:-1
The product of the distinct roots of $$\mid x^2 - x - 6 \mid = x + 2$$ is
correct answer:-1
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
correct answer:-1
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 $$b^2 + c$$?
correct answer:-4
The number of solutions to the equation $$\mid x \mid (6x^2 + 1) = 5x^2$$ is
correct answer:-5
If $$U^{2}+(U-2V-1)^{2}$$= −$$4V(U+V)$$ , then what is the value of $$U+3V$$ ?
correct answer:-3
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
correct answer:-36
If $$x+1=x^{2}$$ and $$x>0$$, then $$2x^{4}$$ is
correct answer:-4
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]
correct answer:-2
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?
correct answer:-2
For which value of k does the following pair of equations yield a unique solution for x such that the solution is positive?
$$x^2 - y^2 = 0$$
$$(x-k)^2 + y^2 = 1$$
correct answer:-3
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 $$p^2 + q^2$$?
correct answer:-4
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
correct answer:-4
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?
correct answer:-2
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?
correct answer:-1
If the equation $$x^3 - ax^2 + bx - a = 0$$ has three real roots, then it must be the case that,
correct answer:-2
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?
correct answer:-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?
correct answer:-4
The value of $$\frac{(1-d^3)}{(1-d)}$$ is
correct answer:-2
The roots of the equation $$ax^{2} + 3x + 6 = 0$$ will be reciprocal to each other if the value of a is
correct answer:-4
If $$xy + yz + zx = 0$$, then $$(x + y + z)^2$$ equals
correct answer:-3
Video solutions can be a helpful resource for candidates preparing for CAT Quadratic Equations questions. They can provide a step-by-step explanation of how to solve the problem, helping candidates better understand the concept and formula.
Usually, the questions in the CAT from Quadratic equations questions are moderately difficult. But not so tough if you are well versed with the basics and practice a good number of questions from this topic.