# JEE Main Problems | QUADRATIC EQUATIONS | 2013 to 2017 | Chapterwise Solutions - Videos

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In this video, we will discuss previous year JEE Main questions of the chapter QUADRATIC EQUATIONS (questions from year 2013 to 2017).
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JEE Main 2013 Online
If α and β are the root of the equation x2 + px + 3p/4 = 0 such that |α-β|=√10, then p belongs to the set
(1) {2, -5} (2) {-3, 2} (3) {-2, 5} (4) {3, -5}

JEE Main 2014
Let α and β be the roots of the equation px2 + qx + r = 0, p ≠ 0. If p, q, r are in AP, and 1/α + 1/β = 4, then the value of |α-β| is equal to

JEE Main 2014 B. Arch.
If the roots of the equation 1/(x+p)+1/(x+q)=1/r are equal in magnitude and opposite in sign, then the
product of the roots is
(1) -(p^2-q^2 )/2 (2) (p^2+q^2 ) (3) (p^2-q^2 )/2 (4) -(p^2+q^2 )/2

JEE Main 2014 Online
If α and β are the roots of the equation x2 – 4√2kx + 2 e^(4 ln⁡k )- 1 = 0, for some k. If α^2+β^2=66, then α^3+β^3 is equal to

JEE Main 2017 B. Arch.
If λ_1 and λ_2 are the two values of λ such that the roots α and β of the quadratic equation
λ(x^2-x)+x+5=0 satisfy: α/β + β/α + 4/5 =0, then λ_1/〖λ_2〗^2 + λ_2/〖λ_1〗^2 is equal to
(1) 488 (2) 536 (3) 512 (4) 504

JEE Main 2015
Let α and β be the roots of the equation x^2-6x-2=0. If a_n=α^n-β^n. Then (a_10-2a_8)/(2a_9 )=
(1) 6 (2) -6 (3) 3 (4) -3

JEE Main 2017 B. Arch. Paper 2
The sum of the abscissa of the points where the curves, y = kx2 + (5k + 3) x + 6k + 5, (k ∈ R), touch the x-axis, is equal to

JEE Main 2016 B. Arch. Paper 2
The number of integral values of m for which the equation, (1 + m2) x2 – 2(1 + 3m)x + (1 + 8m) = 0, has no real root, is:
(1) 1 (2) 2 (3) 3 (4) infinitely many

JEE Main 2013 Online
If p and q are non-zero real numbers and α^3+β^3=-p, αβ=q, then a quadratic equation whose roots are α^2/β and β^2/α is:

JEE Main 2014 Online
If 1/√α and 1/√β are the roots of the equation ax2 + bx + 1 = 0, (a ≠ 0, a, b ∈ R), then the equation
x(x + b3) + (a3 – 3abx) = 0 has roots:
(1) α^(3/2),β^(3/2) (2) αβ^(1/2),α^(1/2) β (3) √αβ,αβ (4) α^(-3/2),β^(-3/2)

JEE Main 2017
If, for a positive integer n, the quadratic equation, x(x + 1) + (x + 1)(x + 2) +…..+ (x + n – 1)(x + n) = 10n has two consecutive integral solutions, then n is equal to

JEE Main 2015 Online
If the two roots of the equation, (a – 1)(x4 + x2 + 1) + (a + 1)(x2 + x + 1)2 = 0 are real and distinct, then the set of all values of ‘a’ is:

JEE Main 2014 Online
The sum of the roots of the equation x^2+|2x-3|-4=0, is:
(1) 2 (2) -2 (3) √2 (4) -√2

JEE Main 2016
The sum of all real values of x satisfying this equation (x^2-5x+5)^((x^2+4x-60) )=1 is
(1) – 4 (2) 6 (3) 5 (4) 3

JEE Main 2015 Online
If 2 + 3i is one of the roots of the equation 2×3 – 9×2 + kx – 13 = 0, k ∈ R, then real root of this equation
(1) exists and is equal to 1 (2) exists and is equal to –1/2
(3) exists and is equal to 1/2 (4) does not exist

JEE Main 2014 Online
If the equations 2×2 + 3x + 4 = 0 and ax2 + bx + c = 0, a,b,c ∈ R, a ≠ 0, have a common root, then a : b : c is
(1) 1 : 2 : 3 (2) 2 : 3 : 4 (3) 4 : 3 : 2 (4) 3 : 2 : 1

JEE Main 2016 Online
If equations x2 + bx -1 = 0 and x2+ x+ b = 0 have a common root different from -1, then |b| is equal to
(1) √2 (2) 2 (3) √3 (4) 3

JEE Main 2013 Online
The value of “a” for which one root of the equation x2 – (a + 1)x + (a2 + a – 8) = 0 exceeds 2, and other is lesser than 2, are given by

JEE Main 2013 B. Arch. Paper 2
If the quadratic equation 3×2 + 2(a2 + 1)x + (a2 – 3a + 2) = 0 possess roots of opposite signs, then “a” lies in the interval

JEE Main 2015 B. Arch. Paper 2
The values of k for which each root of the equation, x2 – 6kx + 2 – 2k + 9k2 = 0 is greater than 3, always satisfy the inequality :

JEE Main 2014 Online
Let p(x) be a quadratic polynomial such that p(0) = 1. If p(x) leaves remainder 4 when divided by (x – 1) and it leaves remainder 6 when divided by (x + 1), then:
(1) p(2) = 11 (2) p(2) = 19 (3) p(-2) = 19 (4) p(-2) = 11

JEE Main 2014
If a ∈ R and the equation -3(x – [x])2 + 2(x – [x]) + a2 = 0 (where [x] denotes greatest integer less than equal to x) has no integral solution, then all the possible values of a lies in the interval
(1) (-2, -1) (2) (-∞, -2) ∪ (2, ∞) (3) (-1, 0) ∪ (0, 1) (4) (1, 2)

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1. Hello sir ….
Sir … I have a doubt regarding JEE Main 2018
……. Actually in school I am in General category but I Have my OBC certificate from UP. Should I choose OBC category while filling JEE mains 2018 appl.form.

In future will it be any problem while taking admission in Colleges because they wil see in my 12th report card that I am in General category but used OBC benefits in JEE MaiN exam…..??

2. Hello sir.please tell me that solving ncert exercise of physics will be benefitial? I want to score 70 marks in Physics section of jee mains.
Also,please tell that by doing objective RD SHARMA thoroughly.can i score 70 marks in jee main maths..

3. Sir agar maine 1 chapter ko 11th me bahut ache se pada aur ush par 800 questions bhi practice kiya but Sir is ise neet ke exams tak saare concept questions yaad kaise rahega kyu ki aage ke bhi chapters padne hai kaise retained rahega 2 saal tak.

4. Sir,iam regularly watching all your vedios and thanks for giving topic wise description…sir can you give some assignments based on jee main previous year's 2013-17 and list of topics from which question are constantly asked in mains exam.

5. Sir, I did not find jee main online last year Q's anywhere. Please help me. I want all the last year Q's of jee mains online of PCM. Since I have opted for CBT Exam.