CAT 2025 Slot 1 QA Question 5

Type-in-the-answer (no negative marking) · Algebra · Polynomials · Try it, then check the answer and solution below.

The number of non-negative integer values of

k

for which the quadratic equation

x^2 - 5x + k = 0

has only integer roots, is

TITA Answer:

⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution

Official Convenor Answer Key: 3

Answer and solution

Answer: 3

📌 Core Concept & Formula

For a quadratic equation

x^2 + bx + c = 0 , the sum of the roots is - b

and the product of the roots is

c

(Vieta's formulas).

🔢 Step-by-Step Solution

Given Equation:

x^2 - 5x + k = 0

Sum of Roots:

r + s = 5

Product of Roots:

r \cdot s = k

Possible Integer Pairs (r, s):

(0, 5):

k = 0

(1, 4):

k = 4

(2, 3): \( k =

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