Your code seems to work if you remove closing > when you open the file. 
use strict;
use warnings;

my ($textFile, $firstString, $secondString) = @ARGV;

open my $text, "<$textFile" or die "Dead";

while(<$text>){
    if(/$firstString/m){
        print $_;
    }
    if(/$secondString/m){
        print $_;
    }
}

[download]
When I pass it its own filename it gives 
$ perl foo.pl foo.pl first second
my ($textFile, $firstString, $secondString) = @ARGV;
my ($textFile, $firstString, $secondString) = @ARGV;
    if(/$firstString/m){
    if(/$secondString/m){

[download]

In reply to Re: Multiple strings in a file by hotpelmen
in thread Multiple strings in a file by The_Last_Monk

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