JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 25 July 2022, Shift 2, Maths Q22

Question 22 of 90 in this shift, Maths question 22 of 30, Section B.

Let

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

f(x)=0

and

fofofof(x)=0

have a common real root, then

f(-3)

is equal to ___________.

Official answer

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

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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.