For this problem, we are given the expression for a quadratic equation and we need to determine the x-intercepts of its graph.
The x-intercepts coincide with the zeros of the equation, which are obtained when f(x) = 0. So we have:
[tex]x^2-4x-21=0[/tex]We need to determine the roots of the equation above.
[tex]\begin{gathered} x_{1,2}=\frac{-(-4)\pm\sqrt{(-4)^2-4\cdot1\cdot(-21)}}{2\cdot1}\\ \\ x_{1,2}=\frac{4\pm\sqrt{16+84}}{2}=\frac{4\pm\sqrt{100}}{2}=\frac{4\pm10}{2}\\ \\ x_1=\frac{4+10}{2}=\frac{14}{2}=7\\ \\ x_2=\frac{4-10}{2}=\frac{-6}{2}=-3 \end{gathered}[/tex]The intercepts are: (-3,0) and (7,0).
