biquadratic

简明释义

英[ˌbaɪkwɒˈdrætɪk]美[ˌbaɪkwɑːdˈrætɪk]

adj. 四次的；四乘幂的

n. 四次方程式；四乘幂

英英释义

单词用法

同义词

反义词

例句

1.D dissertation is concerned with the dynamics of biquadratic polynomials.

本文主要研究双二次多项式的动力系统。

2.The main contents and contributions include: 1 on basis of the defined biorthogonality, we propose several biquadratic cost functions for array-signal blind separation.

主要的研究内容和成果包括以下几个方面：1利用定义双正交原理提出提出了多种用于阵列信号盲分离双二次代价函数。

3.The realization of high-Q switched-capacitor (SC) bandpass biquadratic- joints require very high capacitor spread and larger chip area.

高Q值的开关电容带通双二次节需要很高的电容比和较大的芯片面积。

4.A general biquadratic realization is also proposed with this SI circuit.

据此，得到了SI电路的一般双二次实现。

5.In chapter 3, a one-dimensional isotropic biquadratic Heisenberg spin chain equation is considered.

第三章研究了一个一维的四阶铁磁链方程。

6.The formula shows that the propagation error from biquadratic polynomial is the same as the error from linear polynomial.

公式表明，不完全双二次多项式的DEM传递误差与双线性多项式的传递误差相同。

7.The results show that the maximum of the exchange bias field departs from easy axis with increasing the biquadratic-coupling field or bilinear field.

结果表明：随着双线性耦合场或双二次耦合场的增加，交换偏置场的最大值位置向易轴靠近。

8.The solution to the biquadratic 四次方程 can be found using various algebraic methods.

解决这个biquadratic 四次方程可以使用多种代数方法。

9.To solve a biquadratic 四次方程, you can substitute y = x^2 and then solve the resulting quadratic equation.

要解一个biquadratic 四次方程，你可以用y = x^2进行替换，然后求解得到的二次方程。

10.In mathematics, a biquadratic 四次方程 is an equation of the form ax^4 + bx^2 + c = 0.

在数学中，biquadratic 四次方程是形如ax^4 + bx^2 + c = 0的方程。

11.Graphing a biquadratic 四次方程 can reveal its symmetry about the y-axis.

绘制一个biquadratic 四次方程的图形可以揭示它关于y轴的对称性。

12.The roots of a biquadratic 四次方程 can sometimes be expressed in terms of radicals.

一个biquadratic 四次方程的根有时可以用根式表示。

作文

In the world of mathematics, various types of equations play a crucial role in problem-solving and theoretical exploration. One such significant type is the biquadratic equation, which refers to a polynomial equation of degree four. Understanding biquadratic equations not only enhances one’s algebraic skills but also opens doors to more advanced mathematical concepts. A biquadratic equation can typically be expressed in the form of ax^4 + bx^2 + c = 0, where a, b, and c are constants, and x represents the variable. This specific structure indicates that the highest power of the variable is four, thus categorizing it as a fourth-degree polynomial.To further comprehend the significance of biquadratic equations, let us explore their applications. In physics and engineering, these equations often arise in scenarios involving vibrations and oscillations, where the motion of an object can be modeled using polynomial functions. For instance, when analyzing the behavior of a beam subjected to various forces, engineers may encounter a biquadratic equation that describes the deflection of the beam under load. By solving this equation, they can predict how the beam will respond to different conditions, ensuring safety and efficiency in design.Moreover, biquadratic equations are instrumental in fields like computer graphics, where they help in rendering curves and surfaces. The ability to manipulate and solve biquadratic equations allows graphic designers and programmers to create smooth transitions and realistic animations. As technology continues to advance, the relevance of biquadratic equations in computational algorithms cannot be overstated.Solving a biquadratic equation often involves a clever substitution to simplify the process. By letting y = x^2, the original equation transforms into a quadratic equation: ay^2 + by + c = 0. This simplification allows for the application of the quadratic formula, y = (-b ± √(b² - 4ac)) / (2a), to find the values of y. Once the values of y are determined, one can easily find the corresponding values of x by taking the square root of y. It is essential to consider both the positive and negative roots during this step, as both can yield valid solutions for x.In conclusion, the study of biquadratic equations is a vital aspect of mathematics that extends beyond theoretical knowledge. Their practical applications in various fields highlight the importance of mastering this concept. Whether in engineering, physics, or computer graphics, understanding how to work with biquadratic equations equips individuals with valuable skills that can be applied in real-world situations. As we continue to explore the complexities of mathematics, the biquadratic equation remains a fundamental building block that enriches our understanding of polynomial functions and their vast applications.

在数学的世界中，各种类型的方程在解决问题和理论探索中发挥着至关重要的作用。其中一个重要的类型是biquadratic方程，指的是一个四次多项式方程。理解biquadratic方程不仅增强了一个人的代数技能，还为更高级的数学概念打开了大门。biquadratic方程通常可以用ax^4 + bx^2 + c = 0的形式表示，其中a、b和c是常数，x代表变量。这个特定的结构表明变量的最高幂为四，从而将其归类为四次多项式。为了进一步理解biquadratic方程的重要性，让我们探讨它们的应用。在物理和工程学中，这些方程通常出现在涉及振动和振荡的场景中，其中物体的运动可以用多项式函数建模。例如，在分析一根受各种力作用的梁的行为时，工程师可能会遇到一个描述梁在载荷下挠度的biquadratic方程。通过求解这个方程，他们可以预测梁在不同条件下的反应，从而确保设计的安全性和有效性。此外，biquadratic方程在计算机图形学等领域也具有重要意义，它们有助于渲染曲线和表面。能够操纵和求解biquadratic方程使图形设计师和程序员能够创建平滑的过渡和逼真的动画。随着技术的不断进步，biquadratic方程在计算算法中的相关性不容小觑。求解biquadratic方程通常涉及巧妙的替换以简化过程。通过令y = x^2，原方程转化为一个二次方程：ay^2 + by + c = 0。这种简化允许使用二次公式y = (-b ± √(b² - 4ac)) / (2a)来找到y的值。一旦确定了y的值，就可以通过对y取平方根轻松找到相应的x值。在这个步骤中考虑正负根是至关重要的，因为两者都可能产生有效的x解。总之，研究biquadratic方程是数学的一个重要方面，它超越了理论知识。它们在各个领域的实际应用突显了掌握这一概念的重要性。无论是在工程、物理还是计算机图形学中，理解如何处理biquadratic方程使个人具备了可以应用于现实世界的宝贵技能。随着我们继续探索数学的复杂性，biquadratic方程仍然是丰富我们对多项式函数及其广泛应用理解的基本构件。