Find Root of Quadratic Equation using PHP

A quadratic equation is a second-degree polynomial equation in a single variable, represented as ax^2 + bx + c = 0, where a, b, and c are constants. Solving a quadratic equation involves finding the values of the variable x that satisfy the equation. In this article, we will explore different approaches to finding the roots of quadratic equations in PHP.

Using Quadratic Formula

The quadratic formula is a standard method for solving quadratic equations.

We can implement this formula in PHP to find the roots of a quadratic equation.

PHP

<?php

function solveQuadratic($a, $b, $c) {
    $discriminant = $b**2 - 4*$a*$c;

    if ($discriminant > 0) {
        $root1 = (-$b + sqrt($discriminant)) / (2*$a);
        $root2 = (-$b - sqrt($discriminant)) / (2*$a);
        return [$root1, $root2];
    } else if ($discriminant == 0) {
        $root = -$b / (2*$a);
        return [$root];
    } else {
        return []; // No real roots
    }
}

// Driver code
$a = 1;
$b = -3;
$c = 2;

$roots = solveQuadratic($a, $b, $c);
echo "Roots: " . implode(', ', $roots);

?>

Output

Roots: 2, 1

Using Factoring

Factoring involves expressing the quadratic equation as the product of two linear factors. We can use this method for simple cases where factoring is straightforward.

PHP

<?php

function solveQuadratic($a, $b, $c) {
    $roots = [];

    if ($a != 0) {
        $factor1 = -($b / (2*$a));
        $factor2 = sqrt($b**2 - 4*$a*$c) / (2*$a);

        $roots[] = $factor1 + $factor2;
        $roots[] = $factor1 - $factor2;
    } elseif ($b != 0) {
        $roots[] = -$c / $b;
    }

    return $roots;
}

// Driver code
$a = 1;
$b = -3;
$c = 2;

$roots = solveQuadratic($a, $b, $c);
echo "Roots: " . implode(', ', $roots);

?>

Output

Roots: 2, 1