Answer:
a.
![x=-1,2,\:or\:6](https://img.qammunity.org/2020/formulas/mathematics/high-school/briqr4mkxwexbuw2ke9zfal3sjnlx5iqd4.png)
Explanation:
The given equation is
![x^3-7x^2+4x+12=0](https://img.qammunity.org/2020/formulas/mathematics/high-school/j22r9wjksp314rso972nn2lszyv0hkug8m.png)
To find all real solutions using the x-intercept method, we to graph the corresponding function using a graphing tool.
The corresponding function is;
![f(x)=x^3-7x^2+4x+12](https://img.qammunity.org/2020/formulas/mathematics/high-school/q16pbzwqxkm1m5b2jzxqbqgjao8qgn1wtk.png)
The real solutions to
, are the x-intercepts of the graph of the corresponding function.
From the graph the x-intercepts are
(-1,0),(2,0) and (6,0).
Therefore the real solutions are
![x=-1,2,\:or\:6](https://img.qammunity.org/2020/formulas/mathematics/high-school/briqr4mkxwexbuw2ke9zfal3sjnlx5iqd4.png)