Sorry if I am using the incorrect terminology. I am beginning to learn Mathematics. I had it in school and college but have forgotten most of it, so please be gentle with me if my questions are stupid.
I recall we have a nomenclature for equations based on the highest exponent of the variables in it.
Those with a degree of 1 are called linear equations.
$$2x + 7 = -5$$
With a degree 2 are called quadratic equations.
$$4x^2 + 2x + 3 = 0$$
With a degree of 3 are called cubic.
$$x^3 + 2x^2 + x - 2 = 0$$
There was a universal term applied to all equations with a degree of 4 or above and that's what I forget and that's my question. What are these polynomials / equations called? What's the blanket term?
$$7y^4 - 2y^3 + y^2 - y = 121$$
4 Answers
$\begingroup$The names ''quartic'' and ''quintic'' for polynomials of degree $4$ and $5$ are commonly used (see here, and here). Other terms such as sextic, etc... are less used and usually, for degree $n>5$ the expression $n-$degree polynomial is used.
$\endgroup$ $\begingroup$Fourth degree is called quartic. Fifth quintic. Sixth sextic, and so on via latin. However I think must people who would use "dodecic equation" rather than "12th degree polynomial" would be derided as pompous jackasses.
Quadratic and cubic are common enough to justify terminology. Quartic and quintic can have special theorems and the terminology lends an air of cleverness if not over done. Sextic is really pushing it.
$\endgroup$ 2 $\begingroup$They are overall called polynomials, but there are names for the individual types: $$2x+7=5 \text{ - linear}$$ $$2x^2+3x+2=0 \text{ - quadratic}$$ $$2x^3+4x^2+3x+2=0 \text{ - cubic}$$ $$2x^4+x^3+4x^2+3x+2=0 \text{ - quartic}$$ $$2x^5+5x^4+x^3+4x^2+3x+2=0 \text{ - quintic}$$ And it goes on, with sextic, septic, octic, and others, but it is so much more convenient to just call them polynomials that the only term greater than cubic I have heard is quartic, and the only terms greater than cubic that I have read (in a different mathematical context) are quartic and quintic. So, in general, polynomials is the term you'd want to use. To talk about a sextic equation, for example, you might talk of a polynomial of the sixth degree, or for any equation in general, a polynomial of the $n$th degree.
If you want to read more about the quartic, the quintic, and others, see this website (for quartic), this website (for quintic), this website (for sextic), this website (for septic), and this website (for polynomials in general).
Hope this helps!
$\endgroup$ 1 $\begingroup$For 1 degree ➡ linear equations For 2 degree ➡ quadratic equations For 3 degree ➡ cubic For 4 degree ➡ quartic For 5 degree ➡ quintic For 6 degree ➡ sextic For 7 degree ➡ septic For 8 degree ➡ octatic For 9 degree ➡ nonatic For10 degree ➡ decatic This ten and useful .I know but forget the others.
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