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JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 9 January 2020, Shift 2, Maths Q52

Question 52 of 75 in this shift, Maths question 2 of 25, Section A.

Let

a,b\in\mathbf{R}

,

a\ne0

be such that the equation,

ax^2-2bx+5=0

has a repeated root

\alpha

, which is also a root of the equation,

x^2-2bx-10=0

. If

\beta

is the other root of this equation, then

\alpha^2+\beta^2

is equal to :

(1) $24$
(2) $25$ Official answer
(3) $26$
(4) $28$

Official answer

Option 2

NTA final key (Jan 2020).

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Common Root Condition

Same idea in other shifts

Asked 2× in all

3 Aug 2021, Shift 2 · Q62If the equations $2x^2 + kx - 5 = 0$ and $x^2 - 3x - 4 = 0$ have one root in common, then a value of ' $k$ ' isEasySingle 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.