To write a PHP program that finds the real solutions of a quadratic equation Ax^2 + Bx + C = 0, we need to implement a function that calculates the discriminant, = B^2 - 4AC. Based on the v
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To write a PHP program that finds the real solutions of a quadratic equation $Ax^2 + Bx + C = 0$, we need to implement a function that calculates the discriminant, $\Delta = B^2 - 4AC$. Based on the value of the discriminant, we determine the nature of the solutions:
If $\Delta < 0$: There are no real solutions.
If $\Delta = 0$: There is exactly one real solution, $x = \frac{-B}{2A}$.
If $\Delta > 0$: There are two distinct real solutions, $x_1 = \frac{-B + \sqrt{\Delta}}{2A}$ and $x_2 = \frac{-B - \sqrt{\Delta}}{2A}$.
The program also needs to handle the case where $A=0$, as the equation would no longer be quadratic.
`php
<?php
/**
Solves a quadratic equation of the form Ax^2 + Bx + C = 0
and prints its real solutions.
@param float $a The coefficient of x^2.
@param float $b The coefficient of x.
@param float $c The constant term.
*/
function solveQuadratic($a, $b, $c) {
// Step 1: Check if 'a' is zero. If so, it's not a quadratic equation.
if ($a == 0) {
echo "Error: The coefficient 'a' cannot be zero for a quadratic equation.\n";
return;
}
echo "For the quadratic equation " . $a . "x^2 + " . $b . "x + " . $c . " = 0:\n";
// Step 2: Calculate the discriminant.
$discriminant = ($b $b) - (4 $a * $c);
// Step 3: Determine solutions based on the discriminant's value.
if ($discriminant < 0) {
echo "The discriminant (B^2 - 4AC) is " . $discriminant . ", which is negative.\n";
echo "Therefore, there are no real solutions to the equation.\n";
} else if ($discriminant == 0) {
// One real solution
$x = -$b / (2 * $a);
echo "The discriminant (B^2 - 4AC) is " . $discriminant . ".\n";
echo "The quadratic equation has one real solution: x = " . $x . "\n";
} else { // $discriminant > 0
// Two distinct real solutions
$x1 = (-$b + sqrt($discriminant)) / (2 * $a);
$x2 = (-$b - sqrt($discriminant)) / (2 * $a);
echo "The discriminant (B^2 - 4AC) is " . $discriminant . ".\n";
echo "The quadratic equation has two distinct real solutions:\n";
echo "x1 = " . $x1 . "\n";
echo "x2 = " . $x2 . "\n";
}
}
// Example Usage:
// Test Case 1: Two distinct real solutions (x^2 - 5x + 6 = 0)
echo "--- Test Case 1: x^2 - 5x + 6 = 0 ---\n";
solveQuadratic(1, -5, 6);
echo "\n";
// Test Case 2: One real solution (x^2 + 4x + 4 = 0)
echo "--- Test Case 2: x^2 + 4x + 4 = 0 ---\n";
solveQuadratic(1, 4, 4);
echo "\n";
// Test Case 3: No real solutions (x^2 + x + 1 = 0)
echo "--- Test Case 3: x^2 + x + 1 = 0 ---\n";
solveQuadratic(1, 1, 1);
echo "\n";
// Test Case 4: Coefficient 'a' is zero (not a quadratic equation)
echo "--- Test Case 4: 0x^2 + 2x + 4 = 0 ---\n";
solveQuadratic(0, 2, 4);
echo "\n";
?>
`
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