Question

Range of a rational algebraic function

score 239 · Answer 1 · 2026-04-12 10:45:06

239

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Range of a rational algebraic function

Published on 12 Apr 2026 - 10:45

score 128 · Answer 2 · 2026-04-17 13:27:56

128

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Let $α,β$ be the roots of $x^2-x+p=0$ and $γ,δ$ be the roots of $x^2-4x+q = 0$ where $p$ and $q$ are integers. If $α,β,γ,δ$ are in GP then $p + q$ is?

Published on 17 Apr 2026 - 13:27

score 94 · Answer 3 · 2026-04-16 15:18:50

94

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What properties do have odd quadratic parabola and even cubic parabola? Were they ever described?

Published on 16 Apr 2026 - 15:18

score 200 · Answer 4 · 2026-04-09 02:17:12

200

Views

Finding the discriminant of a quadratic equation from the given information on the roots of a quadratic equation

Published on 09 Apr 2026 - 2:17

score 285 · Answer 5 · 2026-04-16 01:42:50

285

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Why is the discriminant of quadratic $f$, $\Delta \leq 0$, when $f(x) \geq 0 \forall x \in \mathbb{R}$?

Published on 16 Apr 2026 - 1:42

score 51 · Answer 6 · 2026-04-16 07:50:26

51

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Consider the two functions $f(x)=x^2+2bx+9; \; g(x)= 3a(x+b)$. Find area of the coordinates for non-intersecting graph

Published on 16 Apr 2026 - 7:50

score 58 · Answer 7 · 2026-04-13 03:20:12

58

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Find the range of $a$ for the following quadratic equation.

Published on 13 Apr 2026 - 3:20

score 719 · Answer 8 · 2026-04-17 10:32:20

Find the solutions of the equation $\frac{a^2(x-b)(x-c)}{(a-b)(a-c)}+\frac{b^2(x-a)(x-c)}{(b-a)(b-c)}+\frac{c^2(x-a)(x-b)}{(c-a)(c-b)}=3x-2$

score 129 · Answer 9 · 2026-04-15 21:25:21

129

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Range of k for roots of $|x^2-1|+x^2+kx=0$ lying between $(0,2)$

Published on 15 Apr 2026 - 21:25

score 79 · Answer 10 · 2026-04-11 10:37:55

79

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For which $a,b,c$ is the diophantine quadratic equation $ax^2+bx+c=y^2$ soluble?

Published on 11 Apr 2026 - 10:37

score 96 · Answer 11 · 2026-04-14 11:10:25

96

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Finding the maximum and minimum values of $f(x)=|x-1|+|x^2-2x|$ for $x \in [0,2]$

Published on 14 Apr 2026 - 11:10

score 337 · Answer 12 · 2026-04-14 18:56:40

337

Views

If x,y,z are unequal and if $x+y+z=1$, the expression ${(1+x)(1+y)(1+z)\over (1-x)(1-y)(1-z)}$ is greater than(integer)?

Published on 14 Apr 2026 - 18:56

score 251 · Answer 13 · 2026-04-15 21:06:38

251

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The $x^2+ax+b = 0$ has only one solution and this is $x = -1+1/2$. What are the values of $a$ and $b$?

Published on 15 Apr 2026 - 21:06

score 112 · Answer 14 · 2026-04-13 19:23:06

112

Views

Is $x^2-ax+a^x-1$ real and less than $2$?

Published on 13 Apr 2026 - 19:23

score 102 · Answer 15 · 2026-04-15 18:28:28

102

Views

Having a hard time proving this limit

Published on 15 Apr 2026 - 18:28

List Question

Range of a rational algebraic function

Let $α,β$ be the roots of $x^2-x+p=0$ and $γ,δ$ be the roots of $x^2-4x+q = 0$ where $p$ and $q$ are integers. If $α,β,γ,δ$ are in GP then $p + q$ is?

What properties do have odd quadratic parabola and even cubic parabola? Were they ever described?

Finding the discriminant of a quadratic equation from the given information on the roots of a quadratic equation

Why is the discriminant of quadratic $f$, $\Delta \leq 0$, when $f(x) \geq 0 \forall x \in \mathbb{R}$?

Consider the two functions $f(x)=x^2+2bx+9; \; g(x)= 3a(x+b)$. Find area of the coordinates for non-intersecting graph

Find the range of $a$ for the following quadratic equation.

Find the solutions of the equation $\frac{a^2(x-b)(x-c)}{(a-b)(a-c)}+\frac{b^2(x-a)(x-c)}{(b-a)(b-c)}+\frac{c^2(x-a)(x-b)}{(c-a)(c-b)}=3x-2$

Range of k for roots of $|x^2-1|+x^2+kx=0$ lying between $(0,2)$

For which $a,b,c$ is the diophantine quadratic equation $ax^2+bx+c=y^2$ soluble?

Finding the maximum and minimum values of $f(x)=|x-1|+|x^2-2x|$ for $x \in [0,2]$

If x,y,z are unequal and if $x+y+z=1$, the expression ${(1+x)(1+y)(1+z)\over (1-x)(1-y)(1-z)}$ is greater than(integer)?

The $x^2+ax+b = 0$ has only one solution and this is $x = -1+1/2$. What are the values of $a$ and $b$?

Is $x^2-ax+a^x-1$ real and less than $2$?

Having a hard time proving this limit

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