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Algebra -2- Quadratic equation || Quantitative Aptitude || CAT 2021 || 04 May (App update required to attempt this test)

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Question 1

The number of real roots of the equation x⁶ + 4x² – 30 = 0

Question 2

If A and B are the roots of the quadratic equation x² - (k - 3)x - 2k - 1 = 0, where k is some real number, find the minimum value of A² + B² + 7 (TITA)

Question 3

and

are in arithmetic progression, which of the following are the roots of the equation?

Question 4

The minimum possible value of the sum of the squares of the roots of the equation x² + (a + 3)x - (a + 5) = 0 is

Question 5

If f (x) = ax² + bx + c, where a, b, and c are positive integers, and f (0) = 2, f (1) = 10, and f (2) = 28, find the value of x for which f (x) is minimum.

Question 6

f(x) = ax² + bx + c is a quadratic polynomial and the roots of f(x) = 0 are natural numbers such that one root is double of the other root. If ‘c’ is a perfect square, then

Question 7

The number of distinct real roots of the equation

equals (TITA)

Question 8

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

Question 9

Ujakar and Keshav attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4, 3). Keshav 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?

Question 10

For which value of k does the following pair of equations yield a unique solution for x such that the solution is positive?
X² – y² = 0
(x-k)² + y² = 1

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CAT & MBA Quantitative Aptitude

May 17CAT & MBA