Question

how to prove formally that the $\sqrt{x^2}$ is $|x|$, $x$ being a real number?

score 151 · Answer 1 · 2026-03-29 18:34:32

151

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how to prove formally that the $\sqrt{x^2}$ is $|x|$, $x$ being a real number?

Published on 29 Mar 2026 - 18:34

score 329 · Answer 2 · 2026-04-02 09:02:57

329

Views

is a real-coefficients fourth degree polynomial always factorizable in real-coefficients polynomials?

Published on 02 Apr 2026 - 9:02

score 137 · Answer 3 · 2026-04-01 01:16:07

137

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Is there an analytical way to find the number of real positive roots of polynomials of the form $ax^m + bx^2 + x -c = 0$?

Published on 01 Apr 2026 - 1:16

score 147 · Answer 4 · 2019-12-21 17:59:36

147

Views

Do the turning points of the repeated integrals of ln (x) trace out a logarithmic curve with respect to the y-axis?

Published on 21 Dec 2019 - 17:59

score 103 · Answer 5 · 2026-03-29 04:48:03

103

Views

Polynomials such that roots are multiples of coefficients

Published on 29 Mar 2026 - 4:48

score 87 · Answer 6 · 2026-03-25 22:06:32

87

Views

Family of quartics given the only two roots and an extremum

Published on 25 Mar 2026 - 22:06

score 61 · Answer 7 · 2019-12-24 14:05:42

61

Views

solution of function containing two variables

Published on 24 Dec 2019 - 14:05

score 72 · Answer 8 · 2026-03-25 17:39:31

72

Views

$f(x)=x^3-ax^2-ax+1,\;\;|x_1|+|x_2|+|x_3|=3$

Published on 25 Mar 2026 - 17:39

score 196 · Answer 9 · 2019-12-26 08:51:48

196

Views

Does $f{(x)} = a x^4 - x^3 + ax - a$ have exactly $1$ positive root given $a>0$?

Published on 26 Dec 2019 - 8:51

score 217 · Answer 10 · 2019-12-26 09:03:01

217

Views

Is there a cubic polynomial $f(x)$ with real coefficients such that $f$ is monotonic and $f(x)=f^{-1}(x)$ has more than $3$ real roots?

Published on 26 Dec 2019 - 9:03

score 2.5k · Answer 11 · 2026-03-27 18:15:02

2.5k

Views

How calculate the twelfth root of two?

Published on 27 Mar 2026 - 18:15

score 56 · Answer 12 · 2019-12-27 15:56:53

56

Views

Proof that function $F: \mathbb{R}^n \to \mathbb{R}$ has uncountable infinite roots

Published on 27 Dec 2019 - 15:56

score 26 · Answer 13 · 2019-12-28 09:39:55

26

Views

Find the roots $n$ how many broots get from the equation

Published on 28 Dec 2019 - 9:39

score 5.7k · Answer 14 · 2026-04-02 06:19:28

5.7k

Views

Po-Shen Loh's new way of solving quadratic equation

Published on 02 Apr 2026 - 6:19

score 1.5k · Answer 15 · 2019-12-29 13:49:32

1.5k

Views

Roots of $e^{(z^{2})}=1$

Published on 29 Dec 2019 - 13:49

List Question

how to prove formally that the $\sqrt{x^2}$ is $|x|$, $x$ being a real number?

is a real-coefficients fourth degree polynomial always factorizable in real-coefficients polynomials?

Is there an analytical way to find the number of real positive roots of polynomials of the form $ax^m + bx^2 + x -c = 0$?

Do the turning points of the repeated integrals of ln (x) trace out a logarithmic curve with respect to the y-axis?

Polynomials such that roots are multiples of coefficients

Family of quartics given the only two roots and an extremum

solution of function containing two variables

$f(x)=x^3-ax^2-ax+1,\;\;|x_1|+|x_2|+|x_3|=3$

Does $f{(x)} = a x^4 - x^3 + ax - a$ have exactly $1$ positive root given $a>0$?

Is there a cubic polynomial $f(x)$ with real coefficients such that $f$ is monotonic and $f(x)=f^{-1}(x)$ has more than $3$ real roots?

How calculate the twelfth root of two?

Proof that function $F: \mathbb{R}^n \to \mathbb{R}$ has uncountable infinite roots

Find the roots $n$ how many broots get from the equation

Po-Shen Loh's new way of solving quadratic equation

Roots of $e^{(z^{2})}=1$

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