Extending the Null Factor Theorem

1
Extending the Null Factor Theorem
Ex10G Question 1
2
Solutions to f(x)c

• Say I want to find the solution to sinx0.5,
  where -360x360
• I take each side of the equation seperately and
  graph the two functions on the same set of axes,
  as shown below.
• First f(x)sin x note f(x) need not be a trig
  function - it can be any function
• Next y0.5
• I then find all the intersections of the two
  graphs between 360 and 360.
• In this case the solutions are
• x-300, -60, 60, 300
• The equation is said to have multiple solutions

Ex10G Q 2,3,4
3
Solutions to f(x)g(x)

• The solutions to
• Can be found in a similar manner.
• We take each side of the equation separately, and
  graph the two functions
• On the same graph.
• There functions interesect twice
• There are two solutions
• Approximately
• When x-1.05
• When x0.45

Ex 10G Q5-14