$\alpha$ and $\beta$ are real roots of $p^2x^2+2x+p=0$, where $0<p\leq1$. Find the quadratic with roots $1/\alpha+1$ and $1/\beta+1$, in terms of $p$.

score 513 · Answer 10 · 2026-04-15 19:13:17

513

Views

Let $a$ and $b$ be roots of $x^2-7x+2$. Find the value of $a^6 + b^6$.

Published on 15 Apr 2026 - 19:13

score 193 · Answer 11 · 2026-04-17 08:49:51

193

Views

Let $x^2 + 3x +1 = 0$. Is $x^{2048} + \dfrac{1}{x^{2048}}$ divisible by 3?

Published on 17 Apr 2026 - 8:49

score 665 · Answer 12 · 2026-04-15 04:14:07

665

Views

Why do we assume the discriminant to be greater than or equal to zero while calculating the range of a function?

Published on 15 Apr 2026 - 4:14

score 541 · Answer 13 · 2026-04-17 07:02:53

541

Views

A represents the quadratic form $q(x, y) = x^2 + 4xy + y^2 $; for what values of $(x, y) \in \mathbb{R}^2$ is $ q(x, y) =0$?

Published on 17 Apr 2026 - 7:02

score 69 · Answer 14 · 2026-04-13 14:26:50

69

Views

Sub-blocks of matrix quadratic equations

Published on 13 Apr 2026 - 14:26

score 141 · Answer 15 · 2026-04-15 00:02:16

141

Views

If $a^2 + a + 1 = 0$ find $a^3$

Published on 15 Apr 2026 - 0:02

List Question

Find solution of a Polynomial Equation

Can we generalize the quadratic formula to modular arithmetic?

Maximizing and minimizing a function with x and y

Why is the axis of symmetry of a parabola $x=-\dfrac{b}{2a}$?

Consider sequence of numbers $a_r,\;r\geq0\;$ with $a_0=1\;$ and $a_{r+1}^2=1+a_r\cdot a_{r+2}.\;$ Then which of the following is/are true?

Doubt regarding validity of answer in a mod equation question

A question about Quadratic Simultaneous Equations

Inequality with discriminants

$\alpha$ and $\beta$ are real roots of $p^2x^2+2x+p=0$, where $0<p\leq1$. Find the quadratic with roots $1/\alpha+1$ and $1/\beta+1$, in terms of $p$.

Let $a$ and $b$ be roots of $x^2-7x+2$. Find the value of $a^6 + b^6$.

Let $x^2 + 3x +1 = 0$. Is $x^{2048} + \dfrac{1}{x^{2048}}$ divisible by 3?

Why do we assume the discriminant to be greater than or equal to zero while calculating the range of a function?

A represents the quadratic form $q(x, y) = x^2 + 4xy + y^2 $; for what values of $(x, y) \in \mathbb{R}^2$ is $ q(x, y) =0$?

Sub-blocks of matrix quadratic equations

If $a^2 + a + 1 = 0$ find $a^3$

Trending Questions

Popular # Hahtags

Popular Questions