Mathematics And Computer Programming

Solve a quadratic form equation using substitution

Solve 2x⁴ + 4x² + 1 = 0

Let u=x²

Then u² = x⁴

Replace x² with u
Replace x⁴ with u²

Resulting equation is
2u² + 4u + 1 = 0

Solve for u.

u = (-b +/- sqrt(b² - 4ac)/(2a)
u = (-4 + sqrt(4² - 4*2*1))/(2*1)
u = (-4 - sqrt(4² - 4*2*1))/(2*1)

u=(-4+sqrt(8))/2
u=(-4-sqrt(8))/2

x=+/-sqrt(u)
x=sqrt((-4+sqrt(8))/2)
x=sqrt((-4-sqrt(8))/2)
x=-sqrt((-4+sqrt(8))/2)
x=-sqrt((-4-sqrt(8))/2)

Solve a quadratic equation with a computer program.

<?php
$a = 1;
$b = 2;
$c = 1;
$e = sqrt($b*$b-4*$a*$c);
$f = ((-1)*$b - $e)/(2*$a);
$d = ((-1)*$b + $e)/(2*$a);
print "<br>";
print "The Coefficients are<br>";
print "a = ".$a."<br>";
print "b = ".$b."<br>";
print "c = ".$c."<br>";
print "<br>";
print "The equation is ".$a."x^2 + (".$b."x) + (".$c.")= 0<br>";
print "The Solutions Are Given Below<br>";
print "The first solution is " . $d . "<br>";
print "The second solution is " . $f . "<br>";

$a = 10;
$b = 200;
$c = 1;
$e = sqrt($b*$b-4*$a*$c);
$f = ((-1)*$b - $e)/(2*$a);
$d = ((-1)*$b + $e)/(2*$a);
print "<br>";
print "The Coefficients are<br>";
print "a = ".$a."<br>";
print "b = ".$b."<br>";
print "c = ".$c."<br>";
print "<br>";
print "The equation is ".$a."x^2 + (".$b."x) + (".$c.")= 0<br>";
print "The Solutions Are Given Below<br>";
print "The first solution is " . $d . "<br>";
print "The second solution is " . $f . "<br>";
?>