Question

Showing that $f(x)=e^{x-5}-\ln(x-4)-1$ has only one real root

score 49 · Answer 1 · 2019-03-10 00:19:00

49

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Showing that $f(x)=e^{x-5}-\ln(x-4)-1$ has only one real root

Published on 10 Mar 2019 - 0:19

score 2.5k · Answer 2 · 2026-03-28 17:05:26

2.5k

Views

Do cubics always have one real root?

Published on 28 Mar 2026 - 17:05

score 69 · Answer 3 · 2019-03-12 15:53:43

69

Views

Solving equations of the form $c_0 \sin\left(x+p_0\right)+c_1\sin\left(2x+p_1\right)=0$

Published on 12 Mar 2019 - 15:53

score 148 · Answer 4 · 2026-03-28 22:25:48

148

Views

When does a polynomial with integer coefficients have only irrational roots?

Published on 28 Mar 2026 - 22:25

score 104 · Answer 5 · 2026-03-25 06:04:54

104

Views

Obtaining a closed form solution for $\frac{x}{\sin(x)} = a$ on $[0,1)$

Published on 25 Mar 2026 - 6:04

score 53 · Answer 6 · 2019-03-14 18:05:24

53

Views

Zeros of a sum of powers

Published on 14 Mar 2019 - 18:05

score 243 · Answer 7 · 2019-03-16 08:47:37

243

Views

Find all polynomials with coefficients from set $\{-1,1\}$ and which have all their roots real.

Published on 16 Mar 2019 - 8:47

score 56 · Answer 8 · 2026-03-28 15:36:50

56

Views

why do we factor the roots of an equation as $x-x_1$ and not $x+x_2$

Published on 28 Mar 2026 - 15:36

score 101 · Answer 9 · 2026-03-25 15:42:13

101

Views

sum of coefficients of $k(x)$

Published on 25 Mar 2026 - 15:42

score 103 · Answer 10 · 2019-03-16 21:13:56

Find all solutions to the equation $(z+1)^6=z^6$. Express the solutions in simplified rectangular form. Hint: Clearly $z=0$ is not a solution.

score 65 · Answer 11 · 2026-03-28 15:36:44

65

Views

Find values of $a$ such that $x^2+ax+a^2+6a \lt 0$ $\forall$ $x \in (1,2)$

Published on 28 Mar 2026 - 15:36

score 2.2k · Answer 12 · 2019-03-17 23:21:37

2.2k

Views

Why am I allowed to remove $\ln$ from both sides of an equation?

Published on 17 Mar 2019 - 23:21

score 206 · Answer 13 · 2026-03-25 15:12:10

206

Views

What are the necessary conditions for a polynomial Q(X) such that the roots of Q(X) - X are equal to the real roots of a polynomial P?

Published on 25 Mar 2026 - 15:12

score 86 · Answer 14 · 2019-03-19 14:49:53

86

Views

Zero crossings of cont. differentiable function in a compact set.

Published on 19 Mar 2019 - 14:49

score 130 · Answer 15 · 2026-03-25 22:03:09

130

Views

Prove an inequality with positives $a$, $b$ and $c$.

Published on 25 Mar 2026 - 22:03

List Question

Showing that $f(x)=e^{x-5}-\ln(x-4)-1$ has only one real root

Do cubics always have one real root?

Solving equations of the form $c_0 \sin\left(x+p_0\right)+c_1\sin\left(2x+p_1\right)=0$

When does a polynomial with integer coefficients have only irrational roots?

Obtaining a closed form solution for $\frac{x}{\sin(x)} = a$ on $[0,1)$

Zeros of a sum of powers

Find all polynomials with coefficients from set $\{-1,1\}$ and which have all their roots real.

why do we factor the roots of an equation as $x-x_1$ and not $x+x_2$

sum of coefficients of $k(x)$

Find all solutions to the equation $(z+1)^6=z^6$. Express the solutions in simplified rectangular form. Hint: Clearly $z=0$ is not a solution.

Find values of $a$ such that $x^2+ax+a^2+6a \lt 0$ $\forall$ $x \in (1,2)$

Why am I allowed to remove $\ln$ from both sides of an equation?

What are the necessary conditions for a polynomial Q(X) such that the roots of Q(X) - X are equal to the real roots of a polynomial P?

Zero crossings of cont. differentiable function in a compact set.

Prove an inequality with positives $a$, $b$ and $c$.

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