Video Transcript
Find the solution set of the
equation 𝑥 squared is equal to three 𝑥 plus 10.
As we have been asked to find
the solution set of the equation 𝑥 squared is equal to three 𝑥 plus 10, we
must first rearrange it into the form 𝑓 of 𝑥 is equal to zero. Note that we can do this by
subtracting three 𝑥 and 10 from both sides to get 𝑥 squared minus three 𝑥
minus 10 equals zero. Recall that the solutions of
the equation 𝑓 of 𝑥 equals zero are the 𝑥-values of the points where the
graph of the function crosses the 𝑥-axis. We can find these values by
sketching the graph of the function 𝑓 of 𝑥 equals 𝑥 squared minus three 𝑥
minus 10 and finding where it crosses the 𝑥-axis.
We can draw the graph by
setting up a table of values and calculating 𝑓 of 𝑥 for the selected
𝑥-values. Taking values of 𝑥 from
negative three to six, we have the given values of 𝑓 of 𝑥. We can then plot these on the
𝑥𝑦-plane and join them with a smooth curve. It is easily seen that the
curve crosses the 𝑥-axis at 𝑥 equals five and 𝑥 equals negative two. Note that we could have read
off these values directly from our table, which showed that 𝑓 of 𝑥 equals zero
for these two values of 𝑥. We conclude that the solution
set of the equation 𝑥 squared is equal to three 𝑥 plus 10 is negative two,
five.
