Question: Solve by factorisation - OCR - GCSE Maths - Question 15 - 2020 - Paper 1

To solve the equation 3x² - 2x - 5 = 0 by factorisation, we first determine the correct factors.

We can use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Here, a = 3, b = -2, and c = -5. Plugging these values into the formula, we get:

$x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(3)(-5)}}{2(3)}$

$x = \frac{2 \pm \sqrt{4 + 60}}{6}$

$x = \frac{2 \pm \sqrt{64}}{6}$

$x = \frac{2 \pm 8}{6}$

Calculating the two potential solutions:

1. $x = \frac{10}{6} = \frac{5}{3}$
2. $x = \frac{-6}{6} = -1$

Thus, the correct solutions are:

$x = \frac{5}{3} \text{ or } x = -1$