Complex Numbers & Quadratic Equations – JEE Main 2026 PYQ Quiz

Complex Numbers & Quadratic Equations – JEE Main 2026

Complex Numbers and Quadratic Equations are highly scoring chapters in JEE Main Mathematics. Every year 2–3 questions are asked directly from these topics. This quiz contains most repeated PYQs asked in recent JEE Main shifts.

Q1. Let C = {(x,y) | x² − 2ʸ = 2023, x,y ∈ N}. Then ∑(x + y) over all (x,y) ∈ C is:
Correct Answer: 46
Q2. Let α, β be roots of x² − ax − b = 0. Given P₃ = −5√7 i, P₄ = −3√7 i, P₅ = 11√7 i. Find |α⁴ + β⁴|.
Correct Answer: 31
Q3. If x(x+2)(12−k)=2 has equal roots, distance of (k, k/2) from line 3x+4y+5=0 is:
15
12
5√3
15√5
Q4. If z = α + iβ and |z+2| = z + 4(1+i), then equation whose roots are α+β and αβ is:
x² + 2x − 3 = 0
x² + 3x − 4 = 0
x² + x − 12 = 0
x² + 7x + 12 = 0
Q5. If α,β are roots of x² − √2x + 2 = 0, then α¹⁴ + β¹⁴ is:
−64
−64√2
−128√2
−128
Q6. Number of common roots of z¹⁹⁸⁵ + z¹⁰⁰ + 1 = 0 and z³ + 2z² + 2z + 1 = 0 is:
0
2
1
3
Q7. The equation e⁴ˣ + 8e³ˣ + 13e²ˣ − 8eˣ + 1 = 0 has:
two solutions and both are negative
two solutions and one negative
four solutions
no solution
Q8. If α,β are roots of x² + √2x − 8 = 0, Uₙ = αⁿ + βⁿ. Find (U₁₀ + √2U₉)/(2U₈).
Correct Answer: 4
Q9. If α is a root of x² + x + 1 = 0 and ∑(αᵏ + 1/αᵏ)² from k=1 to n = 20, find n.
Correct Answer: 11
Q10. If |(z₁ − 2z₂)/(½ − z̄₁z̄₂)| = 2, then:
z₁ lies on radius ½ or z₂ on radius 1
z₁ on radius ½ and z₂ on radius 1
z₁ on radius 1 or z₂ on radius ½
both on same circle
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