J17

Graphical solution of equations
(Use the graph of example 2.18)
(a)
The curve is the graph of function x 2 – 3x + 2. It crosses the x-axis at points where
x = 1 and x = 2, i.e. these are the points on the curve for which y = 0.
In short, y = 0 when x = 1 and x = 2.
i.e. x 2 – 3x + 2 = 0 when x = 1 and also when x = 2.
Therefore x = 1 and x = 2 are the solutions of the equation x 2 – 3x + 2 = 0.
In general, if y = ax 2 + bx + c, the solutions of ax 2 + bx + c = 0 are the values of x at
the points where the curve crosses the x-axis.
(b) Use the above graph to solve x 2 – 3x + 1 = 0
Equation to be solved is x 2 – 3x + 1 = 0
i.e. x 2 – 3x = -1
substituting x 2 – 3x = -1 in the equation of the curve y = x 2 – 3x + 2,
we get y = x 2 – 3x + 2
= -1 + 2
= 1.
We need the points on the curve when y = 1. Draw the line y = 1 on the same
axes. The values of x at the points of intersection of the line and the curve are the
solution of the equation.
From the graph, values of x are 0.4 and 2.6.