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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 28 July 2022, Shift 2, Maths Q62

Question 62 of 90 in this shift, Maths question 2 of 30, Section A.

Let α,β\alpha,\beta be the roots of the equation x2−2 x+6=0x^2-\sqrt{2}\,x+\sqrt{6}=0 and 1α2+1, 1β2+1\frac{1}{\alpha^2}+1,\ \frac{1}{\beta^2}+1 be the roots of the equation x2+ax+b=0x^2+ax+b=0. Then the roots of the equation x2−(a+b−2)x+(a+b+2)=0x^2-(a+b-2)x+(a+b+2)=0 are :
  1. (1)non-real complex numbers
  2. (2)real and both negativeOfficial answer
  3. (3)real and both positive
  4. (4)real and exactly one of them is positive

Official answer

Option 2

NTA final key.

Chapter
Complex Numbers and Quadratic Equations
Topic
Quadratic Roots
Idea tested
Transformation of Roots

Same idea in other shifts

Asked 2× in all
  1. 4 Apr 2024, Shift 1 · Q3If 2 and 6 are the roots of the equation ax2+bx+1=0ax^2+bx+1=0, then the quadratic equation, whose roots are 12a+b\frac{1}{2a+b} and…EasySingle 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.