Question

Without graphing estimate the x-intercepts of the graph of f(x)=7x^2+9x+1 to the nearest tenth.

Answer 1

The x-intercepts are at -0.1 and -1.2.

We will use the quadratic formula to find these:
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\=\frac{-9\pm \sqrt{9^2-4(7)(1)}}{2(7)}=\frac{-9\pm \sqrt{81-28}}{14} \\ \\=\frac{-9\pm \sqrt{53}}{14}=\frac{-9+\sqrt{53}}{14}\text{ or } \frac{-9-\sqrt{53}}{14} \\ \\=-0.1\text{ or }-1.2$