by Naveen Neredimalli
Wed 05 Jun 2024 05:26 PM
166

Check out the Top Quadratic Equations questions is one of the key topics in the CAT Quant Section (Algebra). 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. Keep practising free CAT mocks where you'll get a fair idea of how questions are asked, and type of questions asked of CAT Quadratic Equation Questions. You 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.

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**

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**

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**

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**

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**

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**

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**

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**

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**

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

correct answer:-**4**

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)?

correct answer:-**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?

correct answer:-**3**

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**

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?

correct answer:-**1**

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

correct answer:-**3**

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

correct answer:-**1**

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

correct answer:-**5**

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**

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