Solving Quadratic Equations Using Go’s Math Functions

In mathematical computations, quadratic equations appear quite frequently. A quadratic equation takes the form of ax² + bx + c = 0, where x represents an unknown variable, and a, b, and c are known coefficients with a ≠ 0. Solving quadratic equations programmatically can be achieved using a variety of methods, one of which involves Go's math functions.

Basics: Quadratic Formula

The quadratic formula, x = (-b ± √(b² - 4ac)) / 2a, provides the roots of a quadratic equation. The expression under the square root, b² - 4ac, is known as the discriminant.

Step 1: Import Necessary Packages

The math package in Go provides the needed functionality for computing square roots.

package main

import (
    "fmt"
    "math"
)

Intermediate: Implementing the Solution

With Go, we can write a function that utilizes the quadratic formula to calculate the solutions.

func solveQuadratic(a, b, c float64) (float64, float64, error) {
    discriminant := b*b - 4*a*c

    if discriminant < 0 {
        return 0, 0, fmt.Errorf("No real roots exist")
    }

    sqrtDiscriminant := math.Sqrt(discriminant)
    root1 := (-b + sqrtDiscriminant) / (2 * a)
    root2 := (-b - sqrtDiscriminant) / (2 * a)

    return root1, root2, nil
}

Advanced: Handling Edge Cases

It’s crucial to handle specific scenarios beyond just positive and negative discriminants:

func solveQuadraticWithEdges(a, b, c float64) (float64, float64, error) {
    if a == 0 {
        return 0, 0, fmt.Errorf("Coefficient 'a' must not be zero")
    }

    discriminant := b*b - 4*a*c

    if discriminant < 0 {
        return 0, 0, fmt.Errorf("No real roots exists")
    } else if discriminant == 0 {
        // One real root
        root := -b / (2 * a)
        return root, root, nil
    }

    // Two real roots
    sqrtDiscriminant := math.Sqrt(discriminant)
    root1 := (-b + sqrtDiscriminant) / (2 * a)
    root2 := (-b - sqrtDiscriminant) / (2 * a)

    return root1, root2, nil
}