Question
What is the minimum possible value of $a^{2}+b^{2}$ so that the polynomial $x^{4}+ax^{3}+bx^{2}+ax+1=0$ has at least 1 root?
Attempt
I divided by $x^{2}$ and got $$x^{2}+\frac{1}{x^{2}}+2+a\left(x+\frac{1}{x}\right)+b-2=0$$ by letting $$x+\frac{1}{x}=X$$
the equation becomes:
$$X^{2}+...
1
Mu (uppercase Μ, lowercase μ; Ancient Greek , Modern Greek μι or μυ ) is the 12th letter of the Greek alphabet. In the system of Greek numerals it has a value of 40. Mu was derived from the Egyptian hieroglyphic symbol for water (𓈖) which had been simplified by the Phoenicians and named after their word for water, to become mem . Letters that arose from mu include the Roman M and the Cyrillic М.
Names
Ancient Greek
Modern Greek
In Modern Greek, the name of the letter is spelled μι and pronounced . In monotonic orthography, the ancient version is written with an acute accent ins...
In statistics, the Pearson product-moment correlation coefficient (sometimes referred to as the PPMCC or PCC, or Pearson's r) is a measure of the linear correlation (dependence) between two variables X and Y, giving a value between +1 and −1 inclusive. It is widely used in the sciences as a measure of the strength of linear dependence between two variables. It was developed by Karl Pearson from a related idea introduced by Francis Galton in the 1880s.
Definition
Pearson's correlation coefficient between two variables is defined as the covariance of the two variables divided by the prod...
