Finding the roots of quadratic equations

Finding the roots of quadratic equations

1. x(x-4) = 0

   • x=0
   • x-4=0 which means x=4
   • OR

2. 3x^2 - 7 = 0

   • Manipulate the equation so x^2 = 7/3
   • therefore x= +/- sq root 7/3

3. x^2-10x+21=0

   • cross method if possible
   • (x-7)(x-3)=0
   • x-7=0 ...x=7
   • OR
   • x-3=0 ...x=3

4. When all else fails, use the quadratic equation

   • Remember the coefficients are substituted NOT the terms
   • Don't be lazy ... Formula line, Substitution line, then start to work it out

5. Completing the square

   • halve the x term & square it
   • add it to both sides of the eqation
   • then it becomes something like the method in the centre top
   • manipulate the equation so coeffient of x^2 is +1