Question

Find all integer values of $m$ such that the equation $\sqrt{9 - x} = \sqrt{3m - x^2 + 9x} - \sqrt{x}$ has exactly four distinct real roots.

score 130 · Answer 1 · 2026-03-29 19:11:43

130

Views

Find all integer values of $m$ such that the equation $\sqrt{9 - x} = \sqrt{3m - x^2 + 9x} - \sqrt{x}$ has exactly four distinct real roots.

Published on 29 Mar 2026 - 19:11

score 176 · Answer 2 · 2020-02-09 17:04:25

176

Views

How is the principal argument of the root of a complex number found where n is not an integer?

Published on 09 Feb 2020 - 17:04

score 310 · Answer 3 · 2020-02-09 20:26:24

310

Views

Location of zeros of the "real part" of a polynomial

Published on 09 Feb 2020 - 20:26

score 363 · Answer 4 · 2026-03-25 06:04:21

363

Views

What is the condition that a cubic equation $x^3+ax^2+bx+c=0$ has exactly three positive real root?

Published on 25 Mar 2026 - 6:04

score 93 · Answer 5 · 2020-02-11 19:20:43

93

Views

Why does the product of two complex conjugate roots give me a real root?

Published on 11 Feb 2020 - 19:20

score 436 · Answer 6 · 2026-02-23 04:57:43

436

Views

how should Cayley's resolvent be used in order to see if a given quintic equation is solvable or not?

Published on 23 Feb 2026 - 4:57

score 52 · Answer 7 · 2026-03-30 20:47:26

52

Views

Solving complex Exponential equations problem

Published on 30 Mar 2026 - 20:47

score 216 · Answer 8 · 2026-03-30 23:00:56

216

Views

Solve the equation $\sqrt[3]{15-x^3+3x^2-3x}=2\sqrt{x^2-4x+2}+3-x$.

Published on 30 Mar 2026 - 23:00

score 76 · Answer 9 · 2026-04-01 17:09:59

76

Views

Why the q th power of a root is again a root？

Published on 01 Apr 2026 - 17:09

score 38 · Answer 10 · 2026-03-28 21:26:58

38

Views

The root of the nth matrix

Published on 28 Mar 2026 - 21:26

score 50 · Answer 11 · 2020-02-14 19:21:39

50

Views

Can the roots of this equation be obtained?

Published on 14 Feb 2020 - 19:21

score 54 · Answer 12 · 2026-03-26 04:51:07

54

Views

the root of $N$th transpose matrix

Published on 26 Mar 2026 - 4:51

score 67 · Answer 13 · 2020-02-15 21:24:31

67

Views

Solve for the roots in the following equations

Published on 15 Feb 2020 - 21:24

score 1.2k · Answer 14 · 2026-03-25 17:36:25

1.2k

Views

Muller's method's initial approximations for non-real roots

Published on 25 Mar 2026 - 17:36

score 161 · Answer 15 · 2026-02-23 12:58:41

161

Views

Show that the polynomial $f(x) = 3x^4 - 2 x^3 + x^2 + ax - 1$ with $a \in \mathbb{R}$ does not have all of its roots real.

Published on 23 Feb 2026 - 12:58

List Question

Find all integer values of $m$ such that the equation $\sqrt{9 - x} = \sqrt{3m - x^2 + 9x} - \sqrt{x}$ has exactly four distinct real roots.

How is the principal argument of the root of a complex number found where n is not an integer?

Location of zeros of the "real part" of a polynomial

What is the condition that a cubic equation $x^3+ax^2+bx+c=0$ has exactly three positive real root?

Why does the product of two complex conjugate roots give me a real root?

how should Cayley's resolvent be used in order to see if a given quintic equation is solvable or not?

Solving complex Exponential equations problem

Solve the equation $\sqrt[3]{15-x^3+3x^2-3x}=2\sqrt{x^2-4x+2}+3-x$.

Why the q th power of a root is again a root？

The root of the nth matrix

Can the roots of this equation be obtained?

the root of $N$th transpose matrix

Solve for the roots in the following equations

Muller's method's initial approximations for non-real roots

Show that the polynomial $f(x) = 3x^4 - 2 x^3 + x^2 + ax - 1$ with $a \in \mathbb{R}$ does not have all of its roots real.

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