Please enable JavaScript.

Coggle requires JavaScript to display documents.

Quadratic equations, Bibliography:, Fernando Martínez Quintero 3A M…

- - - - x = -b ± √ b^2 - 4ac ---------------------------
        ㅤㅤㅤㅤ2
    - - To explain this, we will take this equation as exmple: x^2 - 6x + 8=0
        
        First, you open two parenthesis that will contain the factors. First we have to find the factor of x^2, which are x and x. (x )(x )
        
        Then, you have to search two numbers that added together are equal to the second term coefficient (6) and that multiplied are equal to the third term (8). In this case the numbers are -4 and -2. It is important to take care of the signs. Now we have (x-2)(x-4)
        
        The last thing you have to do is to equal each parentheis to 0 (x-2=0) and (x-4=0). And then just finish it by changing the side of the plain numbers (-2) and (-4), always following the rule of changing their signs. Now we have that x1=2 and x2=4
- - - - When we have this type of equations, we don't have to do anything. x1=0 and x2=0 in every case
  - - - To solve mixed incomplete quadratic equations, we use factorisation by common term
        
        Taking as example this: 5x^2 - 10x = 0
        
        First we search for the common factor, in this case is 5x, because 10 is a multiple of 5 and the x because both terms (5x^2) and (-10x) have x as a factor
        
        Then we have to search which terms multiplied by the common factor are equal to the two terms we are factorising. If we have 5x as a common factor, we have to multiply it by "x" to get the first term, and to get the second term we have to multiply 5x times 2. This would en looking like this: 5x(x - 2)
        
        In this cases x1 (the common factor) is always equal to 0
        
        After that we have to equal the parenthesis to 0: x - 2 = 0, and finally we just change the side of the "-2" respecting the signs rule: x=2
        
        1 more item...
  - - - Solving this case of equations is easy. The goal is to leave the x alone in one side of the equation. We will take as example: 3x^2 - 27 = 0
        
        First we change the side of the second term (-27) respecting the rules of doing that (changing their sign). 3x^2 = 27
        
        Then we move the 3 that is multiplying x^2 to the other side, now dividing 27. x^2= 27/3
        
        Now that we have x^2 = 9, we just have to move the exponent (^2) to the other side, when we move it it changes into a square root. x = √9
        
        Finally, the result is x1= 3 and x2= -3. The result of x1 is the first solving for x, and the result of x2 is the same answer but with the contrary sign