PHP Examples

PHP Program - Find Roots of a Quadratic Equation



A standard form of a quadratic equation is:

ax2 + bx + c = 0

Where:

a, b and c are real numbers and a ≠ 0.

Roots of the equation are:

Roots of quadratic equation

For Example:

The roots of equation x2 + 5x + 4 = 0 is

Roots of quadratic equation

The roots of the equation will be imaginary if D = b2 - 4ac < 0. For example - the roots of equation x2 + 4x + 5 = 0 will be

Roots of quadratic equation

Example: Calculate roots of a Quadratic equation

In the example below, a function called roots is created which takes a, b and c as arguments to calculate the roots of the equation ax2 + bx + c = 0.

<?php
function roots($a, $b, $c) {
  $D = $b*$b - 4*$a*$c;
  if ($D >= 0){
    $x1 = (-$b + sqrt($D))/(2*$a);
    $x2 = (-$b - sqrt($D))/(2*$a);
    echo "Roots are: $x1, $x2 \n";   
  } else {
    $x1 = -$b/(2*$a);
    $x2 = sqrt(-$D)/(2*$a);
    echo "Roots are: $x1 ± $x2 i \n"; 
  }
}

echo "Equation is x*x+5x+4=0\n";
roots(1,5,4);
echo "\nEquation is x*x+4x+5=0\n";
roots(1,4,5);
?>

The above code will give the following output:

Equation is x*x+5x+4=0
Roots are: -1, -4 

Equation is x*x+4x+5=0
Roots are: -2 ± 1 i 




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