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JEE Main 2025 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 2 April 2025, Shift 2, Maths Q21

Question 21 of 75 in this shift, Maths question 21 of 25, Section B.

If the set of all

a \in \mathbf{R} - \{1\}

, for which the roots of the equation

(1-a)x^2 + 2(a-3)x + 9 = 0

are positive is

(-\infty, -\alpha] \cup [\beta, \gamma)

, then

2\alpha + \beta + \gamma

is equal to __________.

Official answer

7

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Location of Roots
Idea tested: Both Roots Positive

Same idea in other shifts

Asked 2× in all

4 Apr 2026, Shift 2 · Q5If the quadratic equation $(\lambda+2)x^2-3\lambda x+4\lambda=0$ , $\lambda\neq-2$ , has two positive roots, then the number of possible…MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.