Solve the quadratic equation plus#

Either way, Babylonian tax calculators would surely have been impressed. To speed adoption, Loh has produced a video about the method. The question now is how widely it will spread and how quickly. The derivation emerged from this process. Loh, who is a mathematics educator and popularizer of some note, discovered his approach while analyzing mathematics curricula for schoolchildren, with the goal of developing new explanations. “Perhaps the reason is because it is actually mathematically nontrivial to make the reverse implication: that always has two roots, and that those roots have sum −B and product C,” he says. So why now? Loh thinks it is related to the way the conventional approach proves that quadratic equations have two roots. None of them appear to have made this step, even though the algebra is simple and has been known for centuries. He has looked at methods developed by the ancient Babylonians, Chinese, Greeks, Indians, and Arabs as well as modern mathematicians from the Renaissance until today. Loh has searched the history of mathematics for an approach that resembles his, without success.

Yet this technique is certainly not widely taught or known.' So this checks out.Loh says he 'would actually be very surprised if this approach has entirely eluded human discovery until the present day, given the 4,000 years of history on this topic, and the billions of people who have encountered the formula and its proof.

Solve the quadratic equation plus#

Which is negative 9, plus 9, does indeed equal 0. Negative 7 times 1, right? That's negative 1 squared. Squared- negative 1 squared is just 1- so this would be Verify for yourself that they satisfy it. Substitute these q's back into this original equation, and So q could be equal to negativeġ, or it could be equal to 9 over 7. Negative 18 divided by negative 14 is equal Negative 2 plus 16 is 14 dividedīy negative 14 is negative 1. Minus, that plus is that plus right there. Or negative 2 minus- right? This is plus 16 over Thing as being equal to negative 2 plus 16 And what's 256? What's the square root of 256? It's 16. Negative 2 plus or minus the square root of- what'sĤ plus 252? It's just 256. Now what does this equal? Well, we have this is equal to And then our denominator,Ģ times negative 7 is negative 14. We have a positive 252 for that part right there. Negative 7 and you have a minus out front. So it's just going to becomeĪ positive number. Here, if we just take the negative 4 times negativeħ times 9, this negative and that negative is going To negative 2 plus or minus the square root of- let's see,Ģ squared is 4- and then if we just take this part right All of that over 2 timesĪ, which is once again negative 7. Of b squared, of 2 squared, minus 4 times a times negativeħ times c, which is 9. Us that the solutions- the q's that satisfy thisĮquation- q will be equal to negative b. And if we look at it, negativeħ corresponds to a. So if we look at the quadraticĮquation that we need to solve here, we can just Take the positive square root and there's another solution Solutions here, because there's one solution where you Square root of b squared minus 4ac- all of that over 2a. X is going to be equal to negative b plus or minus the That the solutions of this equation are going to be Look, if you have a quadratic equation of this form, We could put the 0 on the left hand side.

Now, the quadratic formula, itĪpplies to any quadratic equation of the form. Solve the equation, 0 is equal to negative 7q squared

So you can see we have to use plus or minus, because when you solve a quadratic equation, very often there are two solutions, those being some value, lets call it 'a', and its negative, that is '-a'. We can write these two solutions as x=☒, which means x=2 and x=-2. So this quadratic equation has TWO solutions. I am sure you know that 3x3=9, so x=3 is a solution, right?īut what about -3? (-3)(-3) also equals 9, (-3)(-3)=9, so x=-3 as well. Y=x² is a quadratic expression since it has a x² term and there is no other term with a greater exponent. What is that? It is an expression that has a variable raised to the power 2 AND that the power 2 is the largest power in the expression: eg x²+2x+1 is a quadratic expression, but 2x+1 is not (no x²), nor is x³+x²+2x+1 (the power 3 in x³ is too big.) We used the quadratic equation because we are solving a quadratic expression.