4.2 Solution by Factorisation

Step 1

Identify $a=6, b=-1, c=-2$ .

Step 2

Product $ac = 6 \times (-2) = -12$ . Sum $b = -1$ .

Step 3

We need factors of -12 that sum to -1. The numbers are -4 and 3.

Step 4

Split middle term: $6x^2 - 4x + 3x - 2 = 0$ .

Step 5

Group terms: $(6x^2 - 4x) + (3x - 2)$ .

Step 6

Factor out common terms: $2x(3x - 2) + 1(3x - 2) = 0$ .

Step 7

Combine: $(3x - 2)(2x + 1) = 0$ .

Step 8

Zero Product Property: $3x - 2 = 0 \implies x = 2/3$ OR $2x + 1 = 0 \implies x = -1/2$ .

Final Answer

Roots are $2/3, -1/2$

Input

Matrix

2×2

Select an operation and click Calculate to see results