Forming a Quadratic Equation and Relation between roots and coefficients — CAT Previous-Year Questions
15 previous-year questions on Forming a Quadratic Equation and Relation between roots and coefficients from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.
Forming a Quadratic Equation and Relation between roots and coefficients · CAT PYQs
The roots of α, β of the equation 3x2 + λx - 1 = 0, satisfy = 15.
The value of (α3 + β3)2, is
If x is a positive real number such that x8 + = 47, then the value of x9 + is
A quadratic equation x2 + bx + c = 0 has two real roots. If the difference between the reciprocals of the roots is 1/3, and the sum of the reciprocals of the squares of the roots is 5/9, then the largest possible value of (b + c) is
If (3 + 2√2) is a root of the equation ax2 + bx + c = 0, and (4 + 2√3) is a root of the equation ay2 + my + n = 0, where a, b, c, m and n are integers, then the value of is
Suppose one of the roots of the equation ax2 – bx + c = 0 is 2 + √3, where a, b and c are rational numbers and a ≠ 0. If b = c3 then |a| equals
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?
The minimum possible value of the squares of the roots of the equation: x2 + (a + 3)x – (a + 5) = 0 is
Answer the next 2 questions based on the information given below.
Let f(x) = ax2 + bx + c, where, a, b and c are certain constants and a ≠ 0. It is known that f(5) = −3f(2) and that 3 is a root of f(x) = 0.
What is the other root of f(x) = 0?
Answer the next 2 questions based on the information given below.
Let f(x) = ax2 + bx + c, where, a, b and c are certain constants and a ≠ 0. It is known that f(5) = −3f(2) and that 3 is a root of f(x) = 0.
What is the value of a + b + c?
Each question is followed by two statements, A and B. Answer each question using the following instructions
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
What are the unique values of b and c in the equation 4x2 + bx + c = 0 if one of the roots of the equation is (−1/2)?
A. The second root is 1/2
B. The ratio of c and b is 1
Each question is followed by two statements, A and B. Answer each question using the following instructions
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
Let p and q be the roots of the quadratic equation x2 − (α − 2)x − α − 1 = 0. What is the minimum possible value of p2 + q2?
Answer the following question based on the information given below.
The batting average (BA) of a test batsman is computed from runs scored and innings played-completed innings and incomplete innings (not out) in the following manner:
r1 = number of runs scored in completed innings; n1 = number of completed innings
r2 = number of runs scored in incomplete innings; n2 = number of incomplete innings
BA =
To better assess batsman's accomplishments, the ICC is considering two other measures MBA1 and MBA2 defined as follows:
MBA1 =
MBA2 =
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 root as (3, 2). What will be the exact roots of the original quadratic equation?
Answer the next 3 questions based on the following information.
There are 60 students in a class. These students are divided into three groups A, B and C of 15, 20 and 25 students each. The groups A and C are combined to form group D.
If the roots x1 and x2 of the quadratic equation x2 − 2x + c = 0 also satisfy the equation 7x2 – 4x1 = 47, then which of the following is true?
Direction: Answer the questions based on the following information.
A salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. But, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs. 1,148, but the inventory reduced by 54.
Given the quadratic equation x2 – (A – 3)x – (A – 2), for what value of A will the sum of the squares of the roots be zero?
Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.
One root of x2 + kx – 8 = 0 is square of the other. Then the value of k is