Find the roots of the quadratic equation $2x^2 - 5x + 3 = 0$ by factorisation.
Step-by-Step Solution
Key Concept: Split the middle term: product $= 2 \times 3 = 6$, sum $= -5$. The factors are $-2$ and $-3$.
Stepwise Solution:
$2x^2 - 2x - 3x + 3 = 0 \Rightarrow 2x(x - 1) - 3(x - 1) = 0 \Rightarrow (2x - 3)(x - 1) = 0$. [1.0 Mark]
$2x - 3 = 0$ or $x - 1 = 0 \Rightarrow x = \dfrac{3}{2}$ or $x = 1$. The roots are $1$ and $\dfrac{3}{2}$. [1.0 Mark]
Marking Scheme:
• Splitting middle term and factorising correctly: 1.0 Mark
• Finding roots $x = 1$ and $x = 3/2$: 1.0 Mark
Correct Answer: