JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 26 July 2022, Shift 1, Maths Q21

Question 21 of 90 in this shift, Maths question 21 of 30, Section B.

If for some

\mathrm{p},\ \mathrm{q},\ \mathrm{r} \in \mathbf{R}

, not all have same sign, one of the roots of the equation

(\mathrm{p}^2 + \mathrm{q}^2)x^2 - 2\mathrm{q}(\mathrm{p} + \mathrm{r})x + \mathrm{q}^2 + \mathrm{r}^2 = 0

is also a root of the equation

x^2 + 2x - 8 = 0

, then

\frac{\mathrm{q}^2 + \mathrm{r}^2}{\mathrm{p}^2}

is equal to __________.

Official answer

272

NTA final key.

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

Same idea in other shifts

Asked 5× in all

25 Jul 2022, Shift 2 · Q22Let $f(x)$ be a quadratic polynomial with leading coefficient 1 such that $f(0)=p,p\neq0$ , and $f(1)=\frac{1}{3}$ . If the equations…HardNumerical value
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
26 Aug 2021, Shift 2 · Q81Let $\lambda\neq0$ be in $\mathbf{R}$ . If $\alpha$ and $\beta$ are the roots of the equation $x^2-x+2\lambda=0$ , and $\alpha$ and $\gamma$ …MediumNumerical value
9 Jan 2020, Shift 2 · Q52Let $a,b\in\mathbf{R}$ , $a\ne0$ be such that the equation, $ax^2-2bx+5=0$ has a repeated root $\alpha$ , which is also a root of the…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.