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Saturday, 31 October

JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 6 April 2026, Shift 2, Maths Q2

Question 2 of 75 in this shift, Maths question 2 of 25, Section A.

Consider the quadratic equation (n2−2n+2)x2−3x+(n2−2n+2)2=0(n^2-2n+2)x^2-3x+(n^2-2n+2)^2=0, n∈Rn\in\mathbf{R}. Let α\alpha be the minimum value of the product of its roots and β\beta be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose first term is α\alpha and the common ratio is αβ\frac{\alpha}{\beta}, is :
  1. (1)6137\frac{61}{37}
  2. (2)12181\frac{121}{81}
  3. (3)364243\frac{364}{243}Official answer
  4. (4)1093729\frac{1093}{729}

Official answer

Option 3

NTA final key.

Chapter
Complex Numbers and Quadratic Equations
Topic
Quadratic Roots
Idea tested
Root-Coefficient Relation

Same idea in other shifts

Asked 15× in all
  1. 2 Apr 2026, Shift 1 · Q1Let α,α+2,α∈Z\alpha, \alpha+2, \alpha \in \mathbb{Z}, be the roots of the quadratic equation…HardSingle correct
  2. 5 Apr 2026, Shift 1 · Q1Let a,b∈Ca, b \in \mathbb{C}. Let α,β\alpha, \beta be the roots of the equation x2+ax+b=0x^2 + ax + b = 0. If β−α=11\beta - \alpha = \sqrt{11} and…MediumSingle correct
  3. 5 Apr 2026, Shift 2 · Q1Let α,β\alpha, \beta be the roots of the equation x2−x+p=0x^2-x+p=0 and γ,δ\gamma, \delta be the roots the equation x2−4x+q=0x^2-4x+q=0;…MediumSingle correct
  4. 5 Apr 2026, Shift 2 · Q2Let z1,z2∈Cz_1, z_2 \in \mathbb{C} be the distinct solutions of the equation z2+4z−(1+12i)=0z^2+4z-(1+12i)=0. Then ∣z1∣2+∣z2∣2|z_1|^2+|z_2|^2 is equal to :MediumSingle correct
  5. 3 Apr 2025, Shift 2 · Q4Let the equation x(x+2)(12−k)=2x(x + 2)(12 - k) = 2 have equal roots. Then the distance of the point (k,k2)\left(k, \frac{k}{2}\right) from the line…EasySingle correct
  6. 6 Apr 2024, Shift 1 · Q21Let x1,x2,x3,x4x_1, x_2, x_3, x_4 be the solution of the equation 4x4+8x3−17x2−12x+9=04x^4+8x^3-17x^2-12x+9=0 and…HardNumerical value
  7. 1 Feb 2024, Shift 2 · Q4Let α\alpha and β\beta be the roots of the equation px2+qx−r=0px^2+qx-r=0, where p≠0p\neq 0. If pp, qq and rr be the consecutive terms of a…MediumSingle correct
  8. 8 Apr 2023, Shift 1 · Q3Let α,β,γ\alpha,\beta,\gamma be the three roots of the equation x3+bx+c=0x^3+bx+c=0. If βγ=1=−α\beta\gamma=1=-\alpha, then…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 108 of the 174 JEE Main shifts held from 2017 to 2026.