Second degree equation
Código EMFQ-E0001-I
VIEW:577 DATA:2020-03-20
What is a second degree equation? To answer this question we must understand what a first degree equation is. And what is a first degree equation?
The resolution of a first degree equation is the search for the value that makes the equation true. For example x plus 1 equals zero. So what is the value of x that makes the equation true. If x has a value of minus 1, then the equation is true, since minus 1 plus 1 equals zero. Any other value in the equation becomes false. And as we have seen solving a first degree equation, it is the search for the value that makes the equation true.
Another example would be x plus 2 equal to 0, so the value of x would be minus 2, so that the equation is true.
And what would be a second degree equation? It would be the product of two first degree equations. So if we multiply two first degree equations, we have a second degree equation. We must bear in mind the characteristics of multiplication by zero first. If x multiplies 0, the result is 0, and if 0 multiplies x, the result is also 0. And 0 times 0 is logically equal to 0.
Let's do the following, let's multiply the two first degree equations that we saw. So we have two equations, x plus 1 equals 0 and x plus 2 equals zero. if we multiply we have the factor x plus 1, times the factor x plus 2, and that is equal to 0. And what values does this product of first degree equations become true. Let's determine that -1 is x, so the factor x plus 1 becomes 0, and when it multiplies the value 1, then it is zero, and the equation becomes true, and if the x is minus 2, then we have the factor x plus 2 becomes zero, and the zero that multiplies minus 1 becomes 0, and so the equation also becomes true, so we have two values that make the equation true. Which is both minus 1 and minus 2. Notice that the answer to the first degree equations, separated,
If we know the first degree equations that formed the second degree equation, we can easily determine the roots of the equation. The roots are the values that make the equation true. Now let's make the product of first degree equations, become the way that questions about the second degree equation are asked. For that we must do the distributive of multiplication. The distributive occurs by multiplying each value of the first equation, with each of the second equation. So getting x squared plus 3 x plus 2 this equals 0.
Remember that this equation is the same as the multiplication of the equations, and so the roots, ie the values that zeroed the equation, have to be the same. We will see. Remember that the truth set is minus 1 and minus 2.
If we use minus 1, and replace it, we have 1 minus 3 plus 2 that gives the value 0. Showing that it is a root of the equation. Now we are going to do the same thing with minus 2. That comes in the value of 4 minus 6 plus 2, and again we have the value 0. Notice that we are working on how to solve the equation and always give the correct value. The math for being exact needs to be that way. If something goes wrong then we are doing something wrong.
Now try to look at the equations and the product of the equations, the search in this case is the values minus 1 and minus 2. Trying to look for the equations that formed the second degree equation. For in them we can easily see the values of the truth set.
Another way is to see the sum and product of the roots in a second degree equation. See that we did the distributive in the multiplication of two first degree equations. We know that the roots are minus 1 and minus 2, if we add minus 1 with minus 2 we have minus 3, so we can see in the formula the sum of the roots by the letter S in the formula. Remember that it is the negative value of the sum. But we can see that minus 1 times minus 2 is equal to 2, since the multiplication of two negative values generates a positive value. So we have the letter P for product, which shows us the product of the roots.
Let's say I know that a root is the value of minus 1. So look at the letter P, which is the product, it has the value two, and I know that one of the roots is -1, so I know what product is the multiplication of one by the other, and I know that one of them is minus 1, and that the multiplication with another root generates the value 2, so only the value -2 which multiplied by -1 which generates the value 2. So we have the second root .
Now let's do the same thing with the sum. But now let's say that I don't know the first root, that I know the second that is minus 2. When we look at the equation we see for example that the value 3 is positive, but the S of the sum is negative, so just put negative in the value, and so we have the value of S. So the sum of the values is minus 3, as we know that one of the root values is minus 2, so only by adding minus 1 we get minus 3.
And again we have the roots of minus 1, and minus 2.
And now we begin the much-feared analysis of the Baskara formula. The first thing is to look at the equation and compare the coefficients. Coefficient is the number that multiplies the variables, plus the constant that is in the equation. So the coefficient that compares to the term "a" is the value 1, the "b" is the value 3, and the "c" is the value 2. This is the basic rule to arrive at the answer to the basic formula, a Once knowing these values it is now only necessary to replace values. If we look at the basic formula, we see that it is just a formula for replacing values. In this case the important thing is to be very careful to replace correctly.
Solving the baskara formula we have, for example, the plus and minus symbol together, this means that for each root we have to use the + symbol for one and the minus for the other. And solving the calculations, again we get to the root minus 1, and minus 2.
See that there were several ways to understand the second degree equation. In mathematics there are several ways to solve an exercise, and as we see, we always arrive at the same answer.
But any mistake, however small, can make the exercise response go wrong. So much concentration, logic and care are needed in mathematics.
It may seem like a lot, but it is not. It is only necessary to be very calm, as they are only the analysis of the same thing in different ways.
The resolution of a first degree equation is the search for the value that makes the equation true. For example x plus 1 equals zero. So what is the value of x that makes the equation true. If x has a value of minus 1, then the equation is true, since minus 1 plus 1 equals zero. Any other value in the equation becomes false. And as we have seen solving a first degree equation, it is the search for the value that makes the equation true.
Another example would be x plus 2 equal to 0, so the value of x would be minus 2, so that the equation is true.
And what would be a second degree equation? It would be the product of two first degree equations. So if we multiply two first degree equations, we have a second degree equation. We must bear in mind the characteristics of multiplication by zero first. If x multiplies 0, the result is 0, and if 0 multiplies x, the result is also 0. And 0 times 0 is logically equal to 0.
Let's do the following, let's multiply the two first degree equations that we saw. So we have two equations, x plus 1 equals 0 and x plus 2 equals zero. if we multiply we have the factor x plus 1, times the factor x plus 2, and that is equal to 0. And what values does this product of first degree equations become true. Let's determine that -1 is x, so the factor x plus 1 becomes 0, and when it multiplies the value 1, then it is zero, and the equation becomes true, and if the x is minus 2, then we have the factor x plus 2 becomes zero, and the zero that multiplies minus 1 becomes 0, and so the equation also becomes true, so we have two values that make the equation true. Which is both minus 1 and minus 2. Notice that the answer to the first degree equations, separated,
If we know the first degree equations that formed the second degree equation, we can easily determine the roots of the equation. The roots are the values that make the equation true. Now let's make the product of first degree equations, become the way that questions about the second degree equation are asked. For that we must do the distributive of multiplication. The distributive occurs by multiplying each value of the first equation, with each of the second equation. So getting x squared plus 3 x plus 2 this equals 0.
Remember that this equation is the same as the multiplication of the equations, and so the roots, ie the values that zeroed the equation, have to be the same. We will see. Remember that the truth set is minus 1 and minus 2.
If we use minus 1, and replace it, we have 1 minus 3 plus 2 that gives the value 0. Showing that it is a root of the equation. Now we are going to do the same thing with minus 2. That comes in the value of 4 minus 6 plus 2, and again we have the value 0. Notice that we are working on how to solve the equation and always give the correct value. The math for being exact needs to be that way. If something goes wrong then we are doing something wrong.
Now try to look at the equations and the product of the equations, the search in this case is the values minus 1 and minus 2. Trying to look for the equations that formed the second degree equation. For in them we can easily see the values of the truth set.
Another way is to see the sum and product of the roots in a second degree equation. See that we did the distributive in the multiplication of two first degree equations. We know that the roots are minus 1 and minus 2, if we add minus 1 with minus 2 we have minus 3, so we can see in the formula the sum of the roots by the letter S in the formula. Remember that it is the negative value of the sum. But we can see that minus 1 times minus 2 is equal to 2, since the multiplication of two negative values generates a positive value. So we have the letter P for product, which shows us the product of the roots.
Let's say I know that a root is the value of minus 1. So look at the letter P, which is the product, it has the value two, and I know that one of the roots is -1, so I know what product is the multiplication of one by the other, and I know that one of them is minus 1, and that the multiplication with another root generates the value 2, so only the value -2 which multiplied by -1 which generates the value 2. So we have the second root .
Now let's do the same thing with the sum. But now let's say that I don't know the first root, that I know the second that is minus 2. When we look at the equation we see for example that the value 3 is positive, but the S of the sum is negative, so just put negative in the value, and so we have the value of S. So the sum of the values is minus 3, as we know that one of the root values is minus 2, so only by adding minus 1 we get minus 3.
And again we have the roots of minus 1, and minus 2.
And now we begin the much-feared analysis of the Baskara formula. The first thing is to look at the equation and compare the coefficients. Coefficient is the number that multiplies the variables, plus the constant that is in the equation. So the coefficient that compares to the term "a" is the value 1, the "b" is the value 3, and the "c" is the value 2. This is the basic rule to arrive at the answer to the basic formula, a Once knowing these values it is now only necessary to replace values. If we look at the basic formula, we see that it is just a formula for replacing values. In this case the important thing is to be very careful to replace correctly.
Solving the baskara formula we have, for example, the plus and minus symbol together, this means that for each root we have to use the + symbol for one and the minus for the other. And solving the calculations, again we get to the root minus 1, and minus 2.
See that there were several ways to understand the second degree equation. In mathematics there are several ways to solve an exercise, and as we see, we always arrive at the same answer.
But any mistake, however small, can make the exercise response go wrong. So much concentration, logic and care are needed in mathematics.
It may seem like a lot, but it is not. It is only necessary to be very calm, as they are only the analysis of the same thing in different ways.
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Tags
second degree equation, functions, algebra, equation, baskara, sum and product