Question

Match each entry in List-I to the correct entry in List-II and choose the correct option.

| List-I | List-II |
|--------|--------|
| (P) If $\alpha$ and $\beta$ are the distinct roots of the equation $\mathrm{x}^{2}+\mathrm{x}+1=0$, then the quadratic equation with roots $\frac{1}{(\alpha+1)^{2026}}$ and $\frac{1}{(\beta+1)^{2026}}$ is | (1) $\mathrm{x}^{2}+\mathrm{x}+1=0$ |
| (Q) If $\alpha$ and $\beta$ are the distinct roots of the equation $\mathrm{x}^{2}+\mathrm{x}+1=0$, then the quadratic equation with roots $\frac{1}{(\alpha+1)^{2027}}$ and $\frac{1}{(\beta+1)^{2027}}$ is | (2) $\mathrm{x}^{2}-\mathrm{x}+1=0$ |
| (R) If $\gamma$ and $\delta$ are the distinct roots of the equation $\mathrm{x}^{2}-\mathrm{x}+1=0$, then the value of $\frac{1}{(\gamma-1)^{2026}}+\frac{1}{(\delta-1)^{2026}}$ is | (3) $\mathrm{x}^{2}+\mathrm{x}-1=0$ |
| (S) If p and r are the distinct roots of the equation $\mathrm{x}^{2}+\mathrm{x}-1=0$, then the value of $\frac{1}{(\mathrm{p}+1)^{3}}+\frac{1}{(\mathrm{r}+1)^{3}}$ is | (4) -1 |
| | (5) -4 |

Accepted Answer

(C) (P)→(1), (Q)→(2), (R)→(4), (S)→(5)

Answer

(A) (P)→(1), (Q)→(2), (R)→(5), (S)→(4)

Answer

(B) (P)→(3), (Q)→(1), (R)→(4), (S)→(5)

Answer

(D) (P)→(2), (Q)→(3), (R)→(5), (S)→(4)

List-I	List-II
(P) If $α$ and $β$ are the distinct roots of the equation $x^{2} + x + 1 = 0$ , then the quadratic equation with roots $\frac{1}{( α + 1 ) ^{2026}}$ and $\frac{1}{( β + 1 ) ^{2026}}$ is	(1) $x^{2} + x + 1 = 0$
(Q) If $α$ and $β$ are the distinct roots of the equation $x^{2} + x + 1 = 0$ , then the quadratic equation with roots $\frac{1}{( α + 1 ) ^{2027}}$ and $\frac{1}{( β + 1 ) ^{2027}}$ is	(2) $x^{2} - x + 1 = 0$
(R) If $γ$ and $δ$ are the distinct roots of the equation $x^{2} - x + 1 = 0$ , then the value of $\frac{1}{( γ - 1 ) ^{2026}} + \frac{1}{( δ - 1 ) ^{2026}}$ is	(3) $x^{2} + x - 1 = 0$
(S) If p and r are the distinct roots of the equation $x^{2} + x - 1 = 0$ , then the value of $\frac{1}{( p + 1 ) ^{3}} + \frac{1}{( r + 1 ) ^{3}}$ is	(4) -1
	(5) -4

JEE Advanced · 2026 · 17 May 2026 · Paper 1 · Quadratic Equations and Inequalities

Solution

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