find the value of the product of roots of this quadratic equation

It is given that one of the roots of the quadratic equation : $x^2 + (p + 3)x - p^2 = 0$, where $p$ is a constant, is negative of the other. The question is : find the value of the product of roots.

We know that this equation has at most two roots in the set of reals. Let's denote them with a and -a. Then your equation is x^2-a^2=0. Therefore p must be equal to -3. Hence the equation is x^2-9=0 and the roots are 3 and -3. So the desired product is -9.

Can $X - Y A^\dagger Y^T\succ0$ be written as an LMI where $A^\dagger$ is a pseudoinverse?

Need clarification on implicit differentiation.

Explanation of terminal objects using limits

For a bounded linear operator T, if $||Tx_o||<\epsilon$, then what can we say the norm of $Tx$ for $x \in$ the epsilon ball around $x_o$

Prove that there exists an $x' \in [a,b]$ such that $f(x') = \frac{\int^b_a fg}{\int^b_a g}$ for the given conditions.

finding out if two vectors are perpendicular or parallel

Proving there exists $k$ such that $p(n)p(n+1)=p(k)$

Let $f:A \to \Bbb R^n$ be measurable. Show that $\{x \in \Bbb R^n \mid m(f^{-1}\{x\}) > 0\}$ is a countable set.

Counting ten-digit numbers whose digits are all different and that are divisible by $11111$

convergence of a series with logarithm

Walk through on Distributive Property Discrete Mathematics Problem

Remove Mac OS X from disk without erasing it