Moderate -0.8 Part (a) is straightforward factorization (common factor extraction). Part (b) requires applying the discriminant condition b²-4ac=0 for equal roots, then solving - this is a standard textbook exercise testing recall of the discriminant formula with minimal problem-solving demand. Well below average difficulty for A-level.
4. (a) Solve the equation \(4 x ^ { 2 } + 12 x = 0\).
$$f ( x ) = 4 x ^ { 2 } + 12 x + c ,$$
where \(c\) is a constant.
(b) Given that \(\mathrm { f } ( x ) = 0\) has equal roots, find the value of \(c\) and hence solve \(\mathrm { f } ( x ) = 0\).
4. (a) Solve the equation $4 x ^ { 2 } + 12 x = 0$.
$$f ( x ) = 4 x ^ { 2 } + 12 x + c ,$$
where $c$ is a constant.\\
(b) Given that $\mathrm { f } ( x ) = 0$ has equal roots, find the value of $c$ and hence solve $\mathrm { f } ( x ) = 0$.\\
\hfill \mbox{\textit{Edexcel C1 Q4 [7]}}