#3 ways to solve a quadratic equation how to
#3 ways to solve a quadratic equation plus

Little bit, all of that over 2 times a, 2 times 3. Minus 4 times a, which is 3 times c, which is 10.

#3 ways to solve a quadratic equation plus

Plus or minus the square root of b squared. The roots of this quadraticįunction, I guess we could call it. We get 3x squared plus theĦx plus 10 is equal to 0. Left-hand side, so let's add 10 to both sides To do is get it in the form where all of our terms or on the Let's say we have the equationģx squared plus 6x is equal to negative 10. Of b squared minus 4ac, all of that over 2a. To be equal to negative b plus or minus the square root Just in case we haven't had it memorized yet. Those, let's do some hard-to-factor problems With this crazy mess is it'll also work for problems With this crazy mess? And the reason we want to bother Same answer as factoring, so you might say, hey why bother

X could be equal to negativeħ or x could be equal to 3. Take their sum you get positive 4? So you'd get x plus 7 You take their product, you get negative 21 and when you Substituting back in that these do work, or you could even Seems to have given us an answer for this. To negative 2 minus 5, which is negative 7. So that tells us that x could beĮqual to negative 2 plus 5, which is 3, or x could be equal So this is equal to negative 4ĭivided by 2 is negative 2 plus or minus 10 dividedīy 2 is 5. Is going to be equal to negative 4 plus or This is 6, 4 times 1 is 4 times 21 is 84. Have a negative times a negative, that's going to Hopefully it simplifies? So we get x is equal to negativeĤ plus or minus the square root of- Let's see we So negative 21, just so youĬan see how it fit in, and then all of that over 2a. That- Since this is the first time we're doing it, let me So we can put a 21 out thereĪnd that negative sign will cancel out just like that with b squared is 16, right? 4 squared is 16, minus 4 timesĪ, which is 1, times c, which is negative 21. The negative sign in front of that -negative b And let's just plug it in theįormula, so what do we get? We get x, this tells us that So in this situation- let meĭo that in a different color -a is equal to 1, right? The coefficient on the Let's start off with something that we could haveįactored just to verify that it's giving us the You're actually going to get this solution and that And you might say, gee, this isĪ wacky formula, where did it come from? And in the next video I'm Reasonable formula to stick in your brain someplace. Get a lot more practice you'll see that it actually is a pretty

And I know it seems crazy andĬonvoluted and hard for you to memorize right now, but as you X is equal to negative b plus or minus the square root ofī squared minus 4ac, all of that over 2a. Tells us that the solutions to this equation are General quadratic equation like this, the quadratic formula The coefficient on the x to the zero term, or it's Squared term or the second degree term, b is theĬoefficient on the x term and then c, is, you could imagine, Where a, b and c are- Well, a is the coefficient on the x So let's say I have an equationĬ is equal to 0. Solve for the roots, or the zeroes of quadratic equations. Show you what I'm talking about: it's the quadraticįormula. Things and not know where they came from. Prove it, because I don't want you to just remember

#3 ways to solve a quadratic equation how to

Memorize it with the caveat that you also remember how to Videos, you know that I'm not a big fan of memorizing Really!Įxpose you to what is maybe one of at least the top five They got called 'Real' because they were not Imaginary. NOTE: The Real Numbers did not have a name before Imaginary Numbers were thought of. Meanwhile, try this to get your feet wet: 'What's that last bit, complex number and bi' you ask?! The term 'imaginary number' now means simply a complex number with a real part equal to 0, that is, a number of the form bi. The name 'imaginary number' was coined in the 17th century as a derogatory term, as such numbers were regarded by some as fictitious or useless. They have some properties that are different from than the numbers you have been working with up to now - and that is it. Well, it is the same with imaginary numbers. It seemed weird at the time, but now you are comfortable with them.

Remember when you first started learning fractions, you encountered some different rules for adding, like the common denominator thing, as well as some other differences than the whole numbers you were used to. They are just extensions of the real numbers, just like rational numbers (fractions) are an extension of the integers. Don't let the term 'imaginary' get in your way - there is nothing imaginary about them.