CAT 2023 Linear and Quadratic Equations Question (Hard)

Question

Let and be the two distinct roots of the equation , such that and are the distinct roots of the equation . Then, the value of is

Accepted Answer

Step 1 Given quadratic equation 2x 2 - 6x k 0 Sum of roots Product of roots Step 2 New equation with roots and x 2 px p 0 Sum of roots Product of roots Step 3 Equate sum and product from given conditions Sum of new roots alpha beta alpha beta 3 2 -p quad Product of new roots alpha beta alpha beta 3

CAT 2023

Quantitative

Linear and Quadratic Equations

Hard

Let $\alpha$ and $\beta$ be the two distinct roots of the equation $2x^2 - 6x + k = 0$ , such that $(\alpha + \beta)$ and $\alpha \beta$ are the distinct roots of the equation $x^2 + px + p = 0$ . Then, the value of $8(k - p)$ is

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