In Matthew chapter 13 - a chapter largely composed of parables - the Lord gives the parable of the tares and the wheat:
Matthew 13:24-30
24 Another parable put he forth unto them, saying, The kingdom of heaven is likened unto a man which sowed good seed in his field:
25 But while men slept, his enemy came and sowed tares among the wheat, and went his way.
26 But when the blade was sprung up, and brought forth fruit, then appeared the tares also.
27 So the servants of the householder came and said unto him, Sir, didst not thou sow good seed in thy field? from whence then hath it tares?
28 He said unto them, An enemy hath done this. The servants said unto him, Wilt thou then that we go and gather them up?
29 But he said, Nay; lest while ye gather up the tares, ye root up also the wheat with them.
30 Let both grow together until the harvest: and in the time of harvest I will say to the reapers, Gather ye together first the tares, and bind them in bundles to burn them: but gather the wheat into my barn.
A little later in the chapter, the Lord gives the explanation of this parable to His disciples:
Matthew 13:36-42
36 Then Jesus sent the multitude away, and went into the house: and his disciples came unto him, saying, Declare unto us the parable of the tares of the field.
37 He answered and said unto them, He that soweth the good seed is the Son of man;
38 The field is the world; the good seed are the children of the kingdom; but the tares are the children of the wicked one;
39 The enemy that sowed them is the devil; the harvest is the end of the world; and the reapers are the angels.
40 As therefore the tares are gathered and burned in the fire; so shall it be in the end of this world.
41 The Son of man shall send forth his angels, and they shall gather out of his kingdom all things that offend, and them which do iniquity;
42 And shall cast them into a furnace of fire: there shall be wailing and gnashing of teeth.
As with any passage that mentions Hell, there will be those who wish to use this parable to teach some variation of Salvation by works or obedience. Does this passage teach that all those who "offend" and "do iniquity" (verse 41) will go to Hell, even if they believe in Christ?
Notice that the tares are defined as "the children of the wicked one" (Matthew 13:38), whereas every believer is a "child of God" (Galatians 3:26, John 1:12: 1 John 5:1). Every child of God has inside them a New Man, who is born of "incorruptible seed" (1 Peter 1:23), and "cannot sin" (1 John 3:9, 5:18), and so will never be marked among those that "offend" or "do iniquity". This topic is covered in detail in the article Every Believer Has Two Natures.
However, apart from the new birth, and the imputed righteousness of Jesus Christ (Philippians 3:9), every single person to ever live can be condemned on the basis of "doing iniquity", as we read:
Psalm 130:3-4
3 If thou, Lord, shouldest mark iniquities, O Lord, who shall stand?
4 But there is forgiveness with thee, that thou mayest be feared.
Every single person "does iniquity" (Ecclesiastes 7:20), hence why Christ needed to come to earth in the first place.
If someone wants to try to justify themselves apart from Jesus Christ on this basis, they will fail, because "the wages of sin is death" (Romans 3:23), and "without the shedding of blood, there is no remission" of sins (Hebrews 9:22). God doesn't accept "good behavior" as payment for sin, but rather, a person's only hope is Christ's atonement.
Towards the end of the chapter, the Lord gives a similar parable, but this time likens the event to a net being cast into the sea:
Matthew 13:47-50
47 Again, the kingdom of heaven is like unto a net, that was cast into the sea, and gathered of every kind:
48 Which, when it was full, they drew to shore, and sat down, and gathered the good into vessels, but cast the bad away.
49 So shall it be at the end of the world: the angels shall come forth, and sever the wicked from among the just,
50 And shall cast them into the furnace of fire: there shall be wailing and gnashing of teeth.
The above parable gives us insight into the parable of the tares and the wheat, as we are told that "the wicked" are separated from "the just", which is to say, "the righteous".
This makes it obvious that those who are "tares", or those being "cast away" here, are unbelievers, since apart from Christ, "there is none righteous, no, not one" (Romans 3:10), and trying to establish righteousness before God on the basis of personal holiness, rather than by faith in Christ, is a fatal, irrevocable mistake:
Romans 10:3-4
3 For they being ignorant of God's righteousness, and going about to establish their own righteousness, have not submitted themselves unto the righteousness of God.
4 For Christ is the end of the law for righteousness to every one that believeth.
The only hope that any person has for being counted among the "just" is to have the imputed righteousness of Jesus Christ by faith (Philippians 3:9), because God is "just, and the justifier of him which believeth in Jesus" (Romans 3:26).
It's impossible to get to Heaven on the basis of personal righteousness, and these passages teach nothing contrary to that. They speak to the fact that Christ allows the saved to live amongst false brethren, who will ultimately be separated from the just.