Solver Find A Quadratic Equation Given The Solutions

Source code of 'Find A Quadratic Equation Given The Solutions'

This Solver (Find A Quadratic Equation Given The Solutions) was created by by jim_thompson5910(35256)

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==section input
This solver will show you how to find a quadratic equation given its solutions. For example, if you type in 2 in the first box and then 3 in the second, you'll get the answer {{{x^2-5x+6=0}}}. Solving this last equation will give you the solutions {{{x=2}}} or {{{x=3}}}. So effectively, you're "going backwards" as opposed to simply solving quadratic equations.

Enter the two solutions. If you have only one solution, enter it twice (to show that it is a double root)

Solution 1: x = *[input solution1=2]

Solution 2: x = *[input solution2=3]

Note: For now, please enter integers only. This solver isn't sophisticated enough (yet) to handle fractions or irrational expressions (ie expressions with square roots)

==section solution

perl

sub my_clean
{
  my $exp=$_[0];
  $exp=~s/\-\-/\+/g;
  $exp=~s/\+\-/\-/g;
  $exp=~s/\+1x/\+x/g;
  $exp=~s/\-1x/\-x/g;
  $exp=~s/\+0x//g;
  $exp=~s/\-0x//g;
  return $exp;
}

print " {{{x=$solution1}}} or {{{x=$solution2}}} Start with the given solutions. ";

print " {{{",my_clean("x-$solution1=0"),"}}} or {{{",my_clean("x-$solution2=0"),"}}} Get everything to one side so that only 0 remains on the right side (for both equations). ";

print " {{{(",my_clean("x-$solution1"),")(",my_clean("x-$solution2"),")=0}}} Use the zero product property to combine the equations. ";

my $second_coefficient=(-1*$solution1)+(-1*$solution2);
my $third_coefficient=(-1*$solution1)*(-1*$solution2);
my $ans="x^2+$second_coefficient x+$third_coefficient";
$ans=my_clean($ans);
$ans=~s/\s//g;

print " {{{$ans=0}}} <a href=\"http://www.algebra.com/algebra/homework/Distributive-associative-commutative-properties/foil.solver\">FOIL</a> out the left side. ";

print " So the answer is {{{$ans=0}}} ";

print " To check your work, simply solve {{{$ans=0}}} for x. Doing so will show you that the solutions are {{{x=$solution1}}} or {{{x=$solution2}}}, which confirm the answer. ";

==section output
ans

==section check
  solution1=2 solution2=3 ans=x^2-5x+6