You are possibly restricted as to how you can determine the answer? For instance, one approach is to actually graph the function and see if it crosses the x-axis. Can you use your calculator to do this? If so you will see that "B" does not intersect the x-axis.
If you can't use your calculator, then you might either solve each equation or use the discriminant to determine if the function has REAL roots. If there are real roots, the graph of the equation intersects the x-axis. If there are only imaginary roots, the graph of the equation does not intersect the x-axis.
For instance the equation x[sup:3jiny029]2[/sup:3jiny029]+2x-3=0 does intersect the x-axis because using the discriminant we get...
a=1, b=2, c=-3
and \(\displaystyle \sqrt{b^2-4ac}=\sqrt{4-4(1)(-3)}=\sqrt{16}=4\). The roots are real so the graph of the equation intersects the x-axis.
However the equation x[sup:3jiny029]2[/sup:3jiny029]+2x+3=0 produces...
\(\displaystyle \sqrt{4-4(1)(3)}=\sqrt{4-12}=\sqrt{-8}\) which is an imaginary number, hence the graph of the equation does not intersect the x-axis.
