All Questions
Tagged with real-numbers proof-writing
127
questions
-1
votes
2
answers
145
views
prove quadratic polynomial has no real roots
The problem asks me to prove that a polynomial $f(x)=x^2+ax+b$ has no real roots for some $a,b \in \Bbb{R}$
I started by assuming that $f(x)=x^2+ax+b$ has real roots and therefore the determinant $a^...
- 689
-1
votes
1
answer
54
views
Prove that there exist equal number of irrational numbers between any 2 rational numbers, when the difference between the 2 rational numbers is same. [closed]
Prove that there exist equal number of irrational numbers between any 2 rational numbers, when the difference between the 2 rational numbers is same.
If the assertion is not true then please prove ...
- 3
-1
votes
1
answer
82
views
Polynomial proof in Real numbers [closed]
how to prove that there exists a 2 variable polynomial which is bounded below and the range of values is strict subset from the $\mathbb{R}$.
- 3
-2
votes
2
answers
48
views
A natural number between two reals [closed]
How should I go about proving the following:
$\forall x \in \mathbb{R}, \exists n \in \mathbb{N}$
$ s.t. $
$20(3x^2 - 3x + 2) > 15n > 12(5x^2 - 5x + 2)$
- 319
-3
votes
4
answers
109
views
why is the co-prime part not mentioned in the definition of the rational number?
Proving $\sqrt{2}$ an irrational number is a quite popular exercise, in precalculus courses, but if we look clearly the definition that is introduced, in the beginning of the course, it never ...
- 282
-3
votes
1
answer
67
views
Proving: $a^2 < b^2 ⇔ |a| < |b|$
I started studying mechanical engineering and it works perfectly fine for me but i stumbled across this problem:
$$a^2 < b^2 ⇔ |a| < |b|$$
I found a solution but that took me a full piece of ...
- 932
-3
votes
1
answer
75
views
How can I prove this question?
We know that it is not proved that $e^e$ is transcendental, so neither is the number that $e^{e\sqrt{2}}$. My question is, if one turns out to be, how can it be proved that the other is? Because there ...
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