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
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?
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?
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?
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?
One root of x2 + kx – 8 = 0 is square of the other. Then the value of k is