Edexcel C1 — Question 4 7 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicDiscriminant and conditions for roots
TypeFind k for equal roots
DifficultyModerate -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.
Spec1.02d Quadratic functions: graphs and discriminant conditions1.02f Solve quadratic equations: including in a function of unknown

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 \(\mathrm { f } ( x ) = 0\).

Question 4:
Part (a):
AnswerMarks Guidance
\(4x^2 + 12x = 0 \Rightarrow 4x(x+3) = 0\)M1 A1 M1 for factorising
\(x = 0\) or \(x = -3\)A1
Part (b):
AnswerMarks
For equal roots: \(b^2 - 4ac = 0\)M1
\(12^2 - 4(4)(c) = 0 \Rightarrow 144 - 16c = 0\)A1
\(c = 9\)A1
\(4x^2 + 12x + 9 = 0 \Rightarrow (2x+3)^2 = 0 \Rightarrow x = -\frac{3}{2}\)A1
# Question 4:

## Part (a):
| $4x^2 + 12x = 0 \Rightarrow 4x(x+3) = 0$ | M1 A1 | M1 for factorising |
| $x = 0$ or $x = -3$ | A1 | |

## Part (b):
| For equal roots: $b^2 - 4ac = 0$ | M1 | |
| $12^2 - 4(4)(c) = 0 \Rightarrow 144 - 16c = 0$ | A1 | |
| $c = 9$ | A1 | |
| $4x^2 + 12x + 9 = 0 \Rightarrow (2x+3)^2 = 0 \Rightarrow x = -\frac{3}{2}$ | A1 | |

---
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]}}