I'm working on my math homework right now and I'm stuck on quadratic equations. The pq-formula is supposed to work, but I don't understand how to apply it correctly. Can someone explain it to me step by step?
The most important trick is to divide everything by the number in front of x² beforehand - then the formula works perfectly! 🎯 So if you have, say, 2x² + 8x + 6 = 0, you first divide by 2 and get x² + 4x + 3 = 0, then p = 4 and q = 3. After that it's easy: just plug it into x = -p/2 ± √((p/2)² - q) and you're done. That saves you a ton of headache with fractions otherwise 😊
The pq-formula only works when the equation is in the form x² + px + q = 0 - so the coefficient in front of x² has to be 1. You then plug your p and q values into the formula x = -p/2 ± √((p/2)² - q) and work it out, and you get two solutions (one with plus, one with minus). The most important thing is to get the signs right - if your equation is, say, x² - 5x + 6 = 0, then p = -5 and q = 6, not p = 5.
The most important thing: you need the normal form x² + px + q = 0 first, exactly like I said - but a lot of people forget the next step, which is identifying the values correctly. Make sure p and q are the coefficients with their signs (so if you have x² - 5x + 6 = 0, then p = -5 and q = 6, not p = 5). Then you just plug them into x = -p/2 ± √((p/2)² - q) and work out both solutions - one with plus, one with minus under the square root. The most common mistake is messing up the signs or making a calculation error when you plug them in, so just double-check a few times.
Write the formula big on a piece of paper and stick it next to your desk - if you see it a hundred times, plugging things in will happen automatically. The practical trick nobody mentions: write out your p and q separately before you use the formula, and highlight the signs in color. Most mistakes happen because people forget the p or use the q with the wrong signs - if you first write down the state "okay, p = +4, q = -3", you're safer.
All the previous answers are right, but I want to point out something a lot of people miss: when you identify p and q, pay attention to the signs. If your equation is x² - 5x + 6 = 0, then p = -5 (not +5), and that matters because you plug -p/2 into the formula - that gives you +2.5 instead of -2.5. A lot of people mess this up because they don't carry the minus sign along. Best thing is to write out the equation again and highlight the signs in color before you start plugging in the values.
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