Edexcel C1 — Question 1 3 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCompleting the square and sketching
TypeSolve quartic as quadratic
DifficultyStandard +0.3 This is a quadratic-in-disguise problem requiring substitution u = x², solving the resulting quadratic (likely by factoring or formula), then taking square roots. It's slightly above average for C1 as it requires recognizing the substitution and handling exact form, but it's a standard technique with straightforward execution once the method is identified.
Spec1.02f Solve quadratic equations: including in a function of unknown

Find in exact form the real solutions of the equation $$x^4 = 5x^2 + 14.$$ [3]

AnswerMarks Guidance
\(x^3 - 5x^2 - 14 = 0\), \((x^2 + 2)(x^3 - 7) = 0\)M1
\(x^2 = -2\) (no solutions) or \(7\)A1
\(x = \pm\sqrt[3]{7}\)A1 (3)
$x^3 - 5x^2 - 14 = 0$, $(x^2 + 2)(x^3 - 7) = 0$ | M1 | 
$x^2 = -2$ (no solutions) or $7$ | A1 | 
$x = \pm\sqrt[3]{7}$ | A1 | (3)
Find in exact form the real solutions of the equation
$$x^4 = 5x^2 + 14.$$ [3]

\hfill \mbox{\textit{Edexcel C1  Q1 [3]}}