高次方程的意思、翻譯和例句

是什麼意思

「高次方程」是指其最高次數大於或等於二的多項式方程。這類方程的形式通常為:a_n * x^n + a_(n-1) * x^(n-1) + ... + a_1 * x + a_0 = 0,其中 n ≥ 2,a_n 不為零。高次方程的解法通常比一次方程和二次方程更為複雜,可能需要使用數值方法、圖形法或特殊的代數技巧來解決。

依照不同程度的英文解釋

  1. An equation with a variable raised to a high power.
  2. A math statement where the highest exponent is more than two.
  3. An equation involving terms with variables raised to powers.
  4. A mathematical expression set equal to zero with a degree of two or more.
  5. An algebraic expression where the variable has a degree of two or higher.
  6. A polynomial equation of degree greater than or equal to two.
  7. An equation that involves a variable raised to a power greater than one.
  8. A mathematical relationship that includes a variable raised to a power of two or more.
  9. A polynomial equation characterized by a degree of two or higher, requiring advanced techniques for solutions.
  10. A type of equation where the variable is raised to a power greater than one, often needing complex methods to solve.

相關英文單字或片語的差別與用法

1:Polynomial equation

用法:

這是一種數學方程,其中包含一個或多個變數,並且每個項的指數是非負整數。這類方程的最高次數決定了其性質和解法。高次方程是多項式方程的一種特殊情況,因為它的最高次數大於或等於二,這使得它的解法較為複雜,通常需要使用代數技巧或數值方法。

例句及翻譯:

例句 1:

這個多項式方程的解需要使用數值方法。

The solution to this polynomial equation requires numerical methods.

例句 2:

學習如何解多項式方程是數學的重要一部分。

Learning how to solve polynomial equations is an important part of mathematics.

例句 3:

他們正在研究一個高次多項式方程的特性。

They are studying the properties of a high-degree polynomial equation.

2:Algebraic equation

用法:

這是一種包含變數和常數的數學方程,通常使用代數運算來表示。高次方程是一種特殊類型的代數方程,因為它的變數次數高於一。這類方程可以是線性、二次或更高次的,解法取決於方程的具體形式。

例句及翻譯:

例句 1:

這個代數方程的解法需要一些代數技巧。

The solution to this algebraic equation requires some algebraic skills.

例句 2:

高次代數方程的解通常較為複雜。

The solutions to high-degree algebraic equations are often more complex.

例句 3:

在數學課上,我們學習了如何解代數方程。

In math class, we learned how to solve algebraic equations.