Ans: (a) $9$ (b)$-8$, $5$
- Since the equation $p(x) = 0$ has equal roots, we have$\begin{array}{rcl}
\Delta & = & 0 \\
(12)^2 – 4(4)(c) & = & 0 \\
-16c & = & -144 \\
c & = & 9
\end{array}$ - Sub. $y = 0$ into $y = p(x) – 169$, we have$\begin{array}{rcl}
4x^2 + 12x + 9 – 169 & = & 0 \\
4x^2 + 12x – 160 & = & 0 \\
x^2 + 3x – 40 & = & 0 \\
(x + 8)(x – 5) & = & 0 \\
\end{array}$Therefore, $x = -8$ or $x = 5$.
Hence, the $x$-intercepts of the graph are $-8$ and $5$.
