Challenging +1.2 This question requires applying the generalized binomial theorem to find coefficients, then solving a quadratic equation from the given constraint. While it involves the generalized binomial theorem (a Further Maths topic), the problem is relatively straightforward: write out three coefficient terms, set up one equation from the sum condition, and solve for p. The positive coefficient condition simply selects the valid root. It's harder than a routine C2 binomial expansion but doesn't require deep insight or extensive multi-step reasoning.
1.In the binomial expansion of
$$( 1 - 8 x ) ^ { p } \quad | x | < \frac { 1 } { 8 }$$
where \(p\) is a positive constant,
-the sum of the coefficient of \(x\) and the coefficient of \(x ^ { 2 }\) is equal to the coefficient of \(x ^ { 3 }\)
-the coefficient of \(x ^ { 2 }\) is positive
Determine the value of \(p\) .
\includegraphics[max width=\textwidth, alt={}, center]{a8e9db6b-dfad-4278-82d8-a8fa5ba61008-02_2264_56_315_1977}
1.In the binomial expansion of
$$( 1 - 8 x ) ^ { p } \quad | x | < \frac { 1 } { 8 }$$
where $p$ is a positive constant,\\
-the sum of the coefficient of $x$ and the coefficient of $x ^ { 2 }$ is equal to the coefficient of $x ^ { 3 }$\\
-the coefficient of $x ^ { 2 }$ is positive\\
Determine the value of $p$ .\\
\includegraphics[max width=\textwidth, alt={}, center]{a8e9db6b-dfad-4278-82d8-a8fa5ba61008-02_2264_56_315_1977}
\hfill \mbox{\textit{Edexcel AEA 2024 Q1 [7]}}