Let $p\le q$ be roots of the (real) quadratic equation $x^2+ax+b=0$, $|p|+|q|\ne 0.$ Form the new equation $x^2+px+q=0$, find its real roots (if exist), e...

According to Wikipedia, Dirichlet conditions are $f$ must be absolutely integrable over a period. $f$ must have a finite number of extrema in any given bo...

I'm not sure how the matrix multiplication at the second image works is it a typo or is my understanding of matrix multiplication flawed. Full soluti...

I have a simple question that I need clarification on: If $$\log(a) = \log(b) + c$$ is it true that $$a = b + \exp(c)$$ Is this correct or am I missing so...

I have a question regarding these two terms. I undertand that for a problem to be well-posed, it needs to satisfy three conditions: Existence of solution ...

So this is my process, but I used calculator to check if I got them right or not. and it seems like i got both of them wrong. number 6 supposed to be 36 a...

Let $\triangle ABC$ be a triangle. Let $Γ$ be its circumcircle, and let $I$ be it’s incenter. Let the internal angle bisectors of $∠A,∠B,∠C$ meet $Γ$ in $...

My friend was fiddling around on the triangle when he created an irregular heptagon with it not able to tessellate. He then asked me if I could create an ...

My task requires to find all numbers from $1-1000$ such that they are divisible by $2$ or $3$ and no other primes. I know that $2$ divides even numbers an...

I am currently a Master's student in math. I do very well in my classes, understand the material, can do the proofs w/o having to read the text, etc,...