1
JEE - Sheet (2025)
Quadratic Equations
Most Important JEE PYQs
Single Correct Type Questions 6. Let α and β be the roots of the equation x2 + (2i – 1) = 0.
Then, the value of |α8 + β8| is equal to :
1. Let a, b be the roots of the quadratic equation
α 23 + β23 + α14 + β14 [29 June, 2022 (Shift-I)]
x2 + 6x + 3 =0. Then 15 is equal to
(a) 50 (b) 250
α + β15 + α10 + β10
(c) 1250 (d) 1500
[12 April, 2023 (Shift-I)]
(a) 729 (b) 72 7. Let α and β be the roots of x2 – 6x – 2 = 0. If an= an – βn
(c) 81 (d) 9 a – 2a8
for n ≥ 1, then the value of 10 is:
3a9
2. Let a, b be the roots of the equation x 2 − 2 x + 2 =.
0
Then a14 + b14 is equal to [13 April, 2023 (Shift-II)] [25 Feb, 2021 (Shift-II)]
(a) −64 2 (b) −128 2 (a) 2 (b) 1 (c) 4 (d) 3
(c) –64 (d) –128 8. The number of real roots of the equation
3. The sum of all the roots of the equation |x – 8x +15| – 2x 2 e6 x - e 4 x - 2e3 x - 12e 2 x + e x + 1 =0 is:
+ 7 = 0 is: [6 April, 2023 (Shift-I)] [25 July, 2021 (Shift-I)]
(a) 9 + 3 (b) 11 + 3 (a) 1 (b) 4 (c) 2 (d) 6
(c) 9 − 3 (d) 11 − 3 9. If a and b are the distinct roots of the equation x2 + (3)1/4x
4. Let f(x) be a quadratic polynomial such that f(–2) + f(3) = 0. + 31/2 = 0, then the value of a96(a12 – 1) + b96(b12 – 1) is
If one of the roots of f(x) = 0 is –1 , then the sum of the roots equal to: [20 July, 2021 (Shift-I)]
of f(x) = 0 is equal to: [28 June, 2022 (Shift-II)] (a) 56×325 (b) 28×325 (c) 52×324 (d) 56×324
(a) 11 (b) 7 10. The value of 4+ 1 [17 March, 2021 (Shift-I)]
1
3 3 5+
4+ 1
1
5+
(c) 13 (d) 14 4+
3 3 2 4
(a) 2 + 30 (b) 2 + 30
5. If a, b are the roots of the equation 5 5
) x + 3(3 )
1 2
4 2
(
x2 − 5 + 3
log3 5
−5
log5 3 (log3 5) 3
− 5(log5 3) −1 =
3
0 (c) 4 +
5
30 (d) 5 +
5
30
1 1 11. cosec 18° is a root of the equation:
then the equation, whose roots are
and
,
[31 Aug, 2021 (Shift-I)]
[27 July, 2022 (Shift-II)] (a) x2 + 2x – 4 = 0
(a) 3x – 20x – 12 = 0
2
(b) x2 – 2x + 4 = 0
(b) 3x2 – 10x – 4 = 0 (c) 4x2 + 2x – 1 = 0
(c) 3x2 – 10x + 2 = 0 (d) x2 – 2x – 4 = 0
(d) 3x2 – 20x + 16 = 0
JEE - Sheet (2025)
Quadratic Equations
Most Important JEE PYQs
Single Correct Type Questions 6. Let α and β be the roots of the equation x2 + (2i – 1) = 0.
Then, the value of |α8 + β8| is equal to :
1. Let a, b be the roots of the quadratic equation
α 23 + β23 + α14 + β14 [29 June, 2022 (Shift-I)]
x2 + 6x + 3 =0. Then 15 is equal to
(a) 50 (b) 250
α + β15 + α10 + β10
(c) 1250 (d) 1500
[12 April, 2023 (Shift-I)]
(a) 729 (b) 72 7. Let α and β be the roots of x2 – 6x – 2 = 0. If an= an – βn
(c) 81 (d) 9 a – 2a8
for n ≥ 1, then the value of 10 is:
3a9
2. Let a, b be the roots of the equation x 2 − 2 x + 2 =.
0
Then a14 + b14 is equal to [13 April, 2023 (Shift-II)] [25 Feb, 2021 (Shift-II)]
(a) −64 2 (b) −128 2 (a) 2 (b) 1 (c) 4 (d) 3
(c) –64 (d) –128 8. The number of real roots of the equation
3. The sum of all the roots of the equation |x – 8x +15| – 2x 2 e6 x - e 4 x - 2e3 x - 12e 2 x + e x + 1 =0 is:
+ 7 = 0 is: [6 April, 2023 (Shift-I)] [25 July, 2021 (Shift-I)]
(a) 9 + 3 (b) 11 + 3 (a) 1 (b) 4 (c) 2 (d) 6
(c) 9 − 3 (d) 11 − 3 9. If a and b are the distinct roots of the equation x2 + (3)1/4x
4. Let f(x) be a quadratic polynomial such that f(–2) + f(3) = 0. + 31/2 = 0, then the value of a96(a12 – 1) + b96(b12 – 1) is
If one of the roots of f(x) = 0 is –1 , then the sum of the roots equal to: [20 July, 2021 (Shift-I)]
of f(x) = 0 is equal to: [28 June, 2022 (Shift-II)] (a) 56×325 (b) 28×325 (c) 52×324 (d) 56×324
(a) 11 (b) 7 10. The value of 4+ 1 [17 March, 2021 (Shift-I)]
1
3 3 5+
4+ 1
1
5+
(c) 13 (d) 14 4+
3 3 2 4
(a) 2 + 30 (b) 2 + 30
5. If a, b are the roots of the equation 5 5
) x + 3(3 )
1 2
4 2
(
x2 − 5 + 3
log3 5
−5
log5 3 (log3 5) 3
− 5(log5 3) −1 =
3
0 (c) 4 +
5
30 (d) 5 +
5
30
1 1 11. cosec 18° is a root of the equation:
then the equation, whose roots are
and
,
[31 Aug, 2021 (Shift-I)]
[27 July, 2022 (Shift-II)] (a) x2 + 2x – 4 = 0
(a) 3x – 20x – 12 = 0
2
(b) x2 – 2x + 4 = 0
(b) 3x2 – 10x – 4 = 0 (c) 4x2 + 2x – 1 = 0
(c) 3x2 – 10x + 2 = 0 (d) x2 – 2x – 4 = 0
(d) 3x2 – 20x + 16 = 0
