The solutions of the equation x² + 2x − 15 = 0 are:

1. Write x² + 2x − 15 = (x − a)(x − b), requiring a + b = −2 and ab = −15. 2. Factor pairs of 15: 3 × 5. One must be negative since the product is negative. 3. Trying a = −3, b = 5: a + b = 2, ab = −15 — sum is wrong. 4. Trying a = 3, b = −5: a + b = −2, ab = −15 — both match. 5. So x² + 2x − 15 = (x − 3)(x + 5) and the solutions are 3 and −5. _Source: SCERT Kerala Std X Mathematics Part-2, Chapter 9-11 (pp 227-246, 2019 ed.)._