Quadratic equations and complex numbers appear in JEE Main every year and often combine in a single question. This set drills the relationships between roots and coefficients, the discriminant, powers of i, modulus and argument, cube roots of unity and simple loci in the complex plane, with full solutions.
How to practise: read each question and tap the option you think is correct. You will see right away whether you got it, along with a short explanation, and your score is tracked at the bottom of the screen. This set has 15 questions.
Topics covered in this set
- Sum and product of roots
- Discriminant and nature of roots
- Forming equations from given roots
- Powers of i, modulus and conjugate
- Argument and cube roots of unity
- Loci in the complex plane
JEE Mathematics MCQs with answers and explanations
Q1. If α and β are the roots of x² − 5x + 6 = 0, what is α² + β²?
a) 13
b) 11
c) 36
d) 25
Q2. If α and β are the roots of x² − 5x + 6 = 0, what is 1/α + 1/β?
a) 1/6
b) 5
c) 5/6
d) 6/5
Q3. What is the nature of the roots of 2x² + 3x + 5 = 0?
a) Real and equal
b) Rational
c) Real and distinct
d) Non-real complex conjugates
Q4. For what values of k does x² + kx + 9 = 0 have equal roots?
a) k = ±6
b) k = ±3
c) k = 3 only
d) k = 9
Q5. Which quadratic equation has roots 2 and −3?
a) x² + x − 6 = 0
b) x² − x − 6 = 0
c) x² − 5x + 6 = 0
d) x² + x + 6 = 0
Q6. What is the minimum value of x² − 4x + 7 for real x?
a) 4
b) 3
c) 7
d) −4
Q7. The roots of x² − 3x + 2 = 0 are α and β. Which equation has roots α² and β²?
a) x² − 5x + 4 = 0
b) x² − 5x + 2 = 0
c) x² + 5x + 4 = 0
d) x² − 9x + 4 = 0
Q8. How many real solutions does x² − |x| − 6 = 0 have?
a) 0
b) 1
c) 4
d) 2
Q9. What is the value of i²⁰²⁶?
a) 1
b) −1
c) −i
d) i
Q10. What is the modulus of 3 + 4i?
a) 5
b) 25
c) 7
d) √7
Q11. What is the value of (1 + i)⁸?
a) 16
b) 8
c) 16i
d) −16
Q12. What is the conjugate of (2 + 3i) / (1 − i)?
a) (−1 − 5i) / 2
b) (−1 + 5i) / 2
c) (1 − 5i) / 2
d) (5 − i) / 2
Q13. What is the principal argument of −1 + i√3?
a) 5π/6
b) −π/3
c) 2π/3
d) π/3
Q14. If ω is a non-real cube root of unity, what is (1 + ω)(1 + ω²)?
a) 0
b) 2
c) −1
d) 1
Q15. What is the locus of z satisfying |z − 1| = |z + 1|?
a) A circle of radius 1
b) The line Re z = 1
c) The real axis
d) The imaginary axis
Quick revision notes
- α + β = −b/a, αβ = c/a; α² + β² = (α + β)² − 2αβ.
- D > 0 real distinct, D = 0 equal, D < 0 complex conjugates.
- iⁿ repeats with period 4.
- 1 + ω + ω² = 0 and ω³ = 1.
- |z − a| = |z − b| is the perpendicular bisector of a and b.
Frequently asked questions
Are these JEE previous year questions?
No, they are original practice questions at the JEE Main level.
How do I handle equations with |x|?
Substitute t = |x|, solve for t, and keep only non-negative values before converting back to x.
Why do complex roots come in conjugate pairs?
When the coefficients are real, taking the conjugate of the equation shows that the conjugate of any root is also a root.
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