CAT Previous Year Questions: Quadratic equations

Question for CAT Previous Year Questions: Quadratic equations
Try yourself:If x and y are real numbers such that x2 +  (x - 2y - 1)2 = - 4y (x + y), then the value x − 2y is

[2023]

Question for CAT Previous Year Questions: Quadratic equations
Try yourself:If  then  is equal to

[2023]

*Answer can only contain numeric values
Question for CAT Previous Year Questions: Quadratic equations
Try yourself: The number of integer solutions of equation 2 |x| (x2 + 1) = 5x2 is

[2023]

*Answer can only contain numeric values
Question for CAT Previous Year Questions: Quadratic equations
Try yourself:Let α and β be the two distinct roots of the equation 2x2 - 6x + k =0, such that (α+β) and αβ are the distinct roots of the equation x+ px + p = 0. Then, the value of 8 (k - p) is

[2023]

*Answer can only contain numeric values
Question for CAT Previous Year Questions: Quadratic equations
Try yourself:The equation x3 + (2r+1)x2 + (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

[2023]

Question for CAT Previous Year Questions: Quadratic equations
Try yourself:The sum of all possible values of x satisfying the equation  is

[2023]

*Answer can only contain numeric values
Question for CAT Previous Year Questions: Quadratic equations
Try yourself: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 k/4y + 9y is

[2023]

Question for CAT Previous Year Questions: Quadratic equations
Try yourself:The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is

[2023]

Question for CAT Previous Year Questions: Quadratic equations
Try yourself:The largest real value of a for which the equation |x + a| + |x - 1| = 2 has an infinite number of solutions for x is

[2022]

Question for CAT Previous Year Questions: Quadratic equations
Try yourself:Let a and b be natural numbers. If a2 + ab + a = 14 and b2 + ab + b = 28, then (2a + b) equals

[2022]

Question for CAT Previous Year Questions: Quadratic equations
Try yourself:Let r and c be real numbers. If r and - r are roots of 5x3 + cx2 - 10x + 9 = 0, then c equals

[2022]

*Answer can only contain numeric values
Question for CAT Previous Year Questions: Quadratic equations
Try yourself:The number of solutions of the equation |x|(6x2 + 1) = 5x2 is

[TITA 2019]

Question for CAT Previous Year Questions: Quadratic equations
Try yourself:The product of the distinct roots of |x2 - x - 6| = x + 2 is

[2019]

Question for CAT Previous Year Questions: Quadratic equations
Try yourself:What is the largest positive integer such that  is also positive integer?

[2019]

Question for CAT Previous Year Questions: Quadratic equations
Try yourself:Let A be a real number. Then the roots of the equation x2 - 4x - log2A = 0 are real and distinct if and only if

[2019]

Question for CAT Previous Year Questions: Quadratic equations
Try yourself:The quadratic equation x2 + bx + c = 0 has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of b2 + c?

[2019]

Question for CAT Previous Year Questions: Quadratic equations
Try yourself:If u2 + (u−2v−1)2 = −4v(u + v), then what is the value of u + 3v?

[2018]

Question for CAT Previous Year Questions: Quadratic equations
Try yourself:The minimum possible value of the sum of the squares of the roots of the equation x2 + (a + 3)x - (a + 5) = 0 is

[2017]

The document Quadratic Equations CAT Previous Year Questions with Answer PDF is a part of the CAT Course Quantitative Aptitude (Quant).
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## Quantitative Aptitude (Quant)

183 videos|150 docs|113 tests

## FAQs on Quadratic Equations CAT Previous Year Questions with Answer PDF

 1. How do you solve quadratic equations by factoring?
Ans. To solve a quadratic equation by factoring, you need to set the equation equal to zero, factor the quadratic expression, and then set each factor equal to zero to find the roots.
 2. Can quadratic equations have imaginary roots?
Ans. Yes, quadratic equations can have imaginary roots if the discriminant (b^2 - 4ac) is negative.
 3. What is the quadratic formula used for?
Ans. The quadratic formula is used to find the roots of a quadratic equation ax^2 + bx + c = 0, where a, b, and c are constants.
 4. How do you determine the nature of the roots of a quadratic equation?
Ans. The nature of the roots of a quadratic equation can be determined by looking at the discriminant. If the discriminant is positive, the equation has two real roots. If it is zero, the equation has one real root. If it is negative, the equation has two complex roots.
 5. Can all quadratic equations be factored?
Ans. Not all quadratic equations can be factored using integers. Some quadratic equations may require the quadratic formula or completing the square to find the roots.

## Quantitative Aptitude (Quant)

183 videos|150 docs|113 tests

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