Solving Quadratic Equations : Theory

• • To solve a quadratic in the form x² + bx + c = 0 , factorise the quadratic into 2 brackets 
  • E.g. (x + a) (x + b) = 0 
  • Then solve the brackets individually : (x + a) = 0 , so x = -a 
  • (x + b) = 0 , so x = -b

  
• • To solve a quadratic in the form x² + bx = c , rearrange the quadratic to make it equal to 0  
  • x² + bx - c = 0 
  • Now you can factorise the quadratic

  
• • To solve the quadratic x² - ax = 0 , you would factorise it using a single bracket 
  • In the quadratic equation, x is common to both terms, so you can take it out 
  • x(x - a) = 0  
  • Solve the bracket first : (x - a) = 0 , so x = -a 
  • To solve the other x value, set the number outside the bracket as 0 
  • 0(x - a) = 0 , and as 0 x anything = 0 , x = 0

  
• • To solve the quadratic equation in the form of ax² + bx = 0 , factorise the quadratic into a single bracket  
  • x is common to both terms, so take it out : x(ax + b) = 0 
  • If we set the number outside the bracket to 0, the whole solution will be 0, so x = 0 
  • And for the term inside the bracket, we know that ax + b = 0 
  • So therefore, ax = -b , and x = -b / a

  
• • To solve a quadratic in the form ax² - bx - c = 0 , we factorise the quadratic into 2 brackets
  • If we have a coefficient of x² greater than 1, we find the factors of c, and multiply one of the factors for each combination of factors by the coefficient of x², and then repeat for the other factors 
  • We then choose the 2 factors that equal bx when one of them is multiplied by the coefficient, and then subtracted 
  • Then we solve each bracket individually, to find the value of x