CAT 2023 Linear and Quadratic Equations Question (Hard)

Question

A quadratic equation has two real roots. If the difference between the reciprocals of the roots is , and the sum of the reciprocals of the squares of the roots is , then the largest possible value of is

Accepted Answer

Step 1 Let the roots be r and s. Given 1 r 1 s 40 3 1 r 1 s 536 9 Step 2 We know 1 r 1 s s r rs 40 3 1 r 1 s r s r s 536 9 Let sum r s b, product rs c Then s r c 40 3 s r 40c 3 r s c 536 9 But r s r s 2rs b 2c So b 2c c 536 9 Multiply both sides 9 b 2c 536c 9b 18c 536c 9b 554c b 554c 9 Step 3 Try sm

CAT 2023

Quantitative

Linear and Quadratic Equations

Hard

A quadratic equation $x^2 + bx + c = 0$ has two real roots. If the difference between the reciprocals of the roots is $13\frac{1}{3}$ , and the sum of the reciprocals of the squares of the roots is $59\frac{5}{9}$ , then the largest possible value of $(b + c)$ is:

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