![]() For example, even the relatively simple equation sin(x) = x/2 has no analytical solution. Once we get away from polynomial equations, the situation is even worse. However, it can be proven that there is no general formula for the roots of a fifth or higher order polynomial. There also exist formulas for finding roots of cubic and quartic (fourth order) equations, but they are so complicated that they are hardly ever used. For example, we can use the quadratic formula to find the roots of any quadratic polynomial. Unfortunately, many equations cannot be solved analytically. In the examples below, you can see some of the solving capabilities of Maple. The solve command is not only used for solving for zeros, it can be used to solve other equations as well. If you forget to type in an equation and only type in an expression without setting it equal to zero, Maple automatically sets the expression equal to zero. ![]() Here the ``='' sign is used in the equation, not ``:='' which is used for assignment. The following example illustrates how we can find the roots of the function The basic syntax for the solve command is Once you know how many roots there are, you can use the Maple solve command. First, a plot of the function or expression is needed to determine how many roots there are. Since not every expression can be factored and it is sometimes difficult to get the exact root based on the plot, the best method for finding roots is to use Maple's solving capabilities. The example above shows that cannot be factored, however you can see by the plot that there are infinitely many roots.įinding roots of an expression or a function is the same as solving the equation. You may want to plot the expression first to see if there are any roots. When an expression cannot be factored, this does not necessarily imply that there are no roots. That is, some expressions, when plotted, don't intersect with the -axis at all while others may intersect the -axis infinitely many times. Remember, not every expression has roots. When an expression is already in factored form or cannot be factored, the Maple output is the same expression that was entered. You should try different ranges until you obtain a plot that is acceptable. As the two plot commands show, it is sometimes difficult to see exactly how many roots there are based on the range that is chosen. The plot command is used to verify that there are exactly three roots for this expression. Note that there is only one argument that is necessary for the factor command. The example below shows how to factor and plot the expression Plotting the expression may not give us the exact roots, however it is very useful to see how many roots there actually are. This is not the best method since the root is not always an integer value and therefore, it will be difficult to get the exact roots. Another method for finding roots is to plot the expression and estimate the zeros by looking at where the graph intersects the -axis. ![]() This can be done by using the Maple factor command. ![]() For instance, if it is possible, you could factor the expression and set each factor equal to zero. There are several different methods for finding the roots or the zeros of an expression. The purpose of this lab is to locate roots and find solutions to one equation.įinding roots of a function or an expression Finding roots of a function or an expression.
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