How to implement root finding formula in javascript

The root formula is an important concept in mathematics. It can be used to solve the roots of quadratic equations. In computer science, especially in front-end development, root-finding formulas are widely used in the JavaScript language to calculate various complex interactive components in Web pages.

The root finding formula of first and quadratic equations

The quadratic equation is an equation with the following form: ax2 bx c=0, where a, b, c are all real numbers (where a ≠0).

In mathematics, solving the roots of a quadratic equation requires the calculation of the root formula. The root formula of the quadratic equation is:

x = (-b ± √(b2-4ac)) / 2a

where ± represents the two positive and negative roots, that is:

x1 = (-b √(b2-4ac)) / 2a
x2 = (-b - √(b2-4ac)) / 2a

2. Root formula in JavaScript Application

In JavaScript, the root formula can be used to calculate the position, size, shape and other properties of various interactive components in Web pages. The following is a simple example to illustrate the application of the root formula in JavaScript.

Suppose there is a rectangle whose upper and lower corners are located at the upper left corner and lower right corner of the Web page respectively, and its width, height and angle are known, and the coordinates of its lower left corner and upper right corner are required to be calculated.

First, you can calculate the coordinates of the upper right corner of the rectangle by solving for the coordinates of the lower left corner. Suppose the coordinates of the lower left corner of the rectangle are (x, y), then:

x = w * cos(θ)
y = h * sin(θ)

where, w and h represent the width and height of the rectangle respectively, and θ represents the angle of the rectangle. Next, you can determine the coordinates of the lower left corner of the rectangle by solving for the coordinates of its upper right corner. Suppose the coordinates of the upper right corner of the rectangle are (X, Y), then:

X = x w * sin(θ)
Y = y - h * cos(θ)

Passed The above formula can calculate the coordinates of the lower left corner and upper right corner of the rectangle, thereby determining the position and shape of the rectangle.

3. Code implementation of JS root-finding formula

In JavaScript, the calculation of the root-finding formula can be realized through the following code:

function quadraticEquation(a,b,c ) {
var x1,x2;
if(a===0) {

x1 = x2 = -c/b;

} else {

var delta = b*b - 4*a*c;
if(delta<0) {
  x1 = x2 = NaN;
} else if(delta===0) {
  x1 = x2 = -b/(2*a);
} else {
  x1 = (-b+Math.sqrt(delta))/(2*a);
  x2 = (-b-Math.sqrt(delta))/(2*a);
}

}
return [x1,x2];
}

In the above code, first determine whether a is 0. If a is 0, the equation degenerates into a linear equation of one variable and is solved directly. Otherwise, determine the number of roots of the equation by judging the value of the discriminant delta, and calculate the roots of the equation.

4. Conclusion

The root formula is an important concept in mathematics. It can be used to solve the roots of quadratic equations and is widely used in JavaScript language in computer science. In web page development, root-finding formulas can be used to calculate the position, size, shape and other attributes of various complex interactive components, which brings great convenience to developers.

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