GCSE Maths (AQA)

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Algebra Solving Equations and Inequalities

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4:46 Approximating Solutions
Spec A20
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  • The solution of an equation of the form f(x) = 0 is often a point where f(x) changes from positive to negative or vice versa.
  • We can represent the function graphically by plotting the input values x on the x-axis and the output values f(x) on the y-axis.
  • The graph of y = f(x) can be used to solve the equation f(x) = 0. Any point on the x-axis where y = 0 will give us a solution to the equation.
  • The points immediately to the right of the solution are positive and the points immediately to the left are negative.
  • By noticing where the function changes sign, we can deduce where a solution to the equation is.
  • We can use the method of testing values on either side of the solution to find approximate solutions to equations we can't solve analytically.
  • In the example given, the equation x^3 = x + 3 has a solution between x = 1 and x = 2 because the function changes sign somewhere in between.

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