Variants:
わけがない is used to express strong denial or disbelief – "there is no way that…" or "it is impossible that…". The speaker is convinced that something cannot possibly be true or happen. It carries a sense of emphatic negation based on the speaker's reasoning or common sense.
The word わけ literally means "reason" or "logic," so わけがない literally conveys "there is no reason/logic for…" – i.e., it is logically impossible.
Attach わけがない to the plain form of verbs, adjectives, or nouns + な/である.
In polite speech, わけがない becomes わけがありません.
In casual speech, わけがない is often shortened to わけない or even わきゃない.
Be careful not to confuse わけがない with わけではない, which means "it's not that…" or "it doesn't mean that…" and is used to partially deny something rather than completely reject it. わけがない is a much stronger, more absolute denial.
Also note the difference from はずがない ("it can't be that…"), which expresses the speaker's expectation or logical judgment that something is unlikely. While both express impossibility, わけがない often sounds more emotionally emphatic, while はずがない is based more on expectation or evidence.