Question

Given $ax^2+bx+c=0$ with two real roots, $x_1>x_2$, find a quadratic equation whose roots are $x_1+1$ and $x_2-1$ without solving the first equation

score 124 · Answer 1 · 2020-06-15 21:01:41

Given $ax^2+bx+c=0$ with two real roots, $x_1>x_2$, find a quadratic equation whose roots are $x_1+1$ and $x_2-1$ without solving the first equation

score 467 · Answer 2 · 2020-06-16 05:12:33

467

Views

Pair of linear equation in two variables

Published on 16 Jun 2020 - 5:12

score 49 · Answer 3 · 2020-06-16 05:22:39

49

Views

$ f\left(x^{2}+1\right)=f(x) g(x) $ for every $x \in \mathbb{R},$ then

Published on 16 Jun 2020 - 5:22

score 50 · Answer 4 · 2020-06-16 10:16:45

50

Views

Is it possible to prove $a \in\mathbb R$ in the quadratic?

Published on 16 Jun 2020 - 10:16

score 75 · Answer 5 · 2020-06-16 17:52:56

Can someone explain the solution to "If $x^2+ax−3x−(a+2)=0$ has real and distinct roots, then minimum value of $(a^2+1)/(a^2+2)$ is?"

score 39 · Answer 6 · 2026-03-27 10:30:16

39

Views

Quadratic Function Verbal Problem

Published on 27 Mar 2026 - 10:30

score 171 · Answer 7 · 2020-06-17 00:57:16

171

Views

Application of quadratic functions

Published on 17 Jun 2020 - 0:57

score 61 · Answer 8 · 2020-06-17 05:34:11

61

Views

Find all possible values $m$ such that $f(x)=x^2-5mx+10m-4$ has 2 roots and one of them is twice as the other

Published on 17 Jun 2020 - 5:34

score 106 · Answer 9 · 2026-04-02 10:33:02

106

Views

Show that, there are no integers $(m, n)$ such that, $m^2 + (m + 1)^2 = n^4 + (n + 1)^4$.

Published on 02 Apr 2026 - 10:33

score 132 · Answer 10 · 2020-06-17 20:12:50

132

Views

Where did 3.5 come from?

Published on 17 Jun 2020 - 20:12

score 101 · Answer 11 · 2026-03-25 10:57:24

101

Views

Prove $\frac{a^2}{(a+b)^2} \geqslant \frac{4a^2-b^2-bc+7ca}{4(a+b+c)^2}$

Published on 25 Mar 2026 - 10:57

score 199 · Answer 12 · 2020-06-20 05:09:55

199

Views

The set of all real number x such that $||3-x|-| x+2||=5$

Published on 20 Jun 2020 - 5:09

score 119 · Answer 13 · 2020-06-20 23:20:37

119

Views

Solving $\frac{x^2 + 12x + 4}{x+2} = 6\sqrt x$

Published on 20 Jun 2020 - 23:20

score 61 · Answer 14 · 2020-06-21 09:23:18

61

Views

Find Solution set of $(\log_4x)^2+4\sqrt{(\log_4x)^2-\log_2x-4}=\log_2x+16$

Published on 21 Jun 2020 - 9:23

score 228 · Answer 15 · 2026-03-27 08:57:30

228

Views

$A$ could've done a job in 6 hours longer, $B$ in 15 hours longer and $C$ in twice the time needed if they work together. How long together?

Published on 27 Mar 2026 - 8:57

List Question

Given $ax^2+bx+c=0$ with two real roots, $x_1>x_2$, find a quadratic equation whose roots are $x_1+1$ and $x_2-1$ without solving the first equation

Pair of linear equation in two variables

$ f\left(x^{2}+1\right)=f(x) g(x) $ for every $x \in \mathbb{R},$ then

Is it possible to prove $a \in\mathbb R$ in the quadratic?

Can someone explain the solution to "If $x^2+ax−3x−(a+2)=0$ has real and distinct roots, then minimum value of $(a^2+1)/(a^2+2)$ is?"

Quadratic Function Verbal Problem

Application of quadratic functions

Find all possible values $m$ such that $f(x)=x^2-5mx+10m-4$ has 2 roots and one of them is twice as the other

Show that, there are no integers $(m, n)$ such that, $m^2 + (m + 1)^2 = n^4 + (n + 1)^4$.

Where did 3.5 come from?

Prove $\frac{a^2}{(a+b)^2} \geqslant \frac{4a^2-b^2-bc+7ca}{4(a+b+c)^2}$

The set of all real number x such that $||3-x|-| x+2||=5$

Solving $\frac{x^2 + 12x + 4}{x+2} = 6\sqrt x$

Find Solution set of $(\log_4x)^2+4\sqrt{(\log_4x)^2-\log_2x-4}=\log_2x+16$

$A$ could've done a job in 6 hours longer, $B$ in 15 hours longer and $C$ in twice the time needed if they work together. How long together?

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