JEE Main Maths · Complex Numbers and Quadratic Equations

Newton's Sums

Newton's Sums (Complex Numbers and Quadratic Equations) was asked 9 times in 9 JEE Main shifts, 2020–2026, out of the 42 shifts Lumi analysed. 3 of the 9 had a numerical answer.

Times asked: 9; in 9 shifts
Years: 2020–2026
Usual format: Single correct; Multi-step
Pattern: Asked most years; repeats across shifts

How it is asked

Value from roots of linked quadratics
Sum of powers of quadratic roots

Difficulty

Easy 2Medium 7Hard 0

Where it sits

Chapter: Complex Numbers and Quadratic Equations. Topic: Quadratic Roots, 46 questions over 19 ideas.

All 9 questions

Newest first, each with its options and official answer.

6 Apr 2026, Shift 2 · Q3Let $S=\{z\in\mathbb{C}: z^2+\sqrt{6}\,iz-3=0\}$ . Then $\sum_{z\in S} z^8$ is equal to :MediumSingle correct
2 Apr 2025, Shift 1 · Q17Let $P_n=\alpha^n+\beta^n$ , $n\in\mathbf{N}$ . If $P_{10}=123$ , $P_9=76$ , $P_8=47$ and $P_1=1$ , then the quadratic equation having roots…MediumSingle correct
3 Apr 2025, Shift 1 · Q3Let $\alpha$ and $\beta$ be the roots of $x^2 + \sqrt{3}x - 16 = 0$ , and $\gamma$ and $\delta$ be the roots of $x^2 + 3x - 1 = 0$ . If…MediumSingle correct
6 Apr 2024, Shift 2 · Q21Let $\alpha,\beta$ be roots of $x^2+\sqrt{2}x-8=0$ . If $U_n=\alpha^n+\beta^n$ , then $\frac{U_{10}+\sqrt{2}U_9}{2U_8}$ is equal to ________.EasyNumerical value
9 Apr 2024, Shift 2 · Q3Let $\alpha, \beta;\ \alpha>\beta$ , be the roots of the equation $x^2-\sqrt{2}x-\sqrt{3}=0$ . Let $P_n=\alpha^n-\beta^n,\ n\in\mathbb{N}$ .…MediumSingle correct
11 Apr 2023, Shift 1 · Q24If $a$ and $b$ are the roots of the equation $x^2 - 7x - 1 = 0$ , then the value of…MediumNumerical value
13 Apr 2023, Shift 2 · Q3Let $\alpha, \beta$ be the roots of the equation $x^2-\sqrt{2}x+2=0$ . Then $\alpha^{14}+\beta^{14}$ is equal toMediumSingle correct
25 Jul 2021, Shift 1 · Q90If $\alpha,\beta$ are roots of the equation $x^2+5(\sqrt2)x+10=0$ , $\alpha>\beta$ and $P_n=\alpha^n-\beta^n$ for each positive integer n,…MediumNumerical value
2 Sep 2020, Shift 1 · Q52Let $\alpha$ and $\beta$ be the roots of the equation, $5x^{2}+6x-2=0$ . If $S_n=\alpha^{n}+\beta^{n}$ , $n=1, 2, 3, \ldots$ , then :EasySingle correct