What is Quadratic Equation?
A quadratic equation is a type of polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is a variable. Quadratic equations have two solutions, which are called the roots of the equation. The solutions can be real or complex numbers, depending on the values of the constants a, b, and c.
Quadratic equations are commonly used to model various phenomena in mathematics, physics, and engineering
Create a Javascript program to solve Quadratic Equation
Here’s a JavaScript program that will solve a quadratic equation of the form ax^2 + bx + c = 0:
function solveQuadratic(a, b, c) {
let x1, x2;
let discriminant = b * b - 4 * a * c;
if (discriminant > 0) {
x1 = (-b + Math.sqrt(discriminant)) / (2 * a);
x2 = (-b - Math.sqrt(discriminant)) / (2 * a);
console.log(`Roots are real and different.`);
console.log(`x1 = ${x1} , x2 = ${x2}`);
} else if (discriminant == 0) {
x1 = (-b) / (2 * a);
console.log(`Roots are real and same.`);
console.log(`x1 = x2 =${x1}`);
} else {
console.log(`Roots are complex and different.`);
}
}
solveQuadratic(1, -3, 2); // Roots are real and different. x1 = 2 , x2 = 1
Now let’s understand the explanation of this program
The function first declares two variables, x1 and x2, which will be used to store the roots of the equation if they exist.
Next, the function calculates the discriminant (b^2 – 4ac) and stores it in a variable called discriminant. This value will be used to determine the type of roots that the equation has.
The function then enters a if block, which checks if the discriminant is greater than 0. If this is the case, then the roots of the equation are real and different. The function calculates the roots using the formula (-b +- sqrt(discriminant)) / 2a, and stores the results in x1 and x2. It then prints a message indicating that the roots are real and different, and prints the values of x1 and x2.
If the discriminant is not greater than 0, then the function enters an else if block that checks if the discriminant is equal to 0. If this is the case, then the roots of the equation are real and the same. The function calculates the root using the formula -b / 2a, and stores the result in x1. It then prints a message indicating that the roots are real and the same, and prints the value of x1.
If the discriminant is not equal to 0, then the function enters the final else block, which means that the roots of the equation are complex and different. It prints a message indicating this.
Finally, the function is called with the arguments 1, -3, and 2, which corresponds to the equation x^2 – 3x + 2 = 0. The output is:
Roots are real and different.
x1 = 2 , x2 = 1
This indicates that the roots of the equation are 2 and 1.
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