(a) 2, −5
Factorising: $x^2 + 3x - 10 = (x-2)(x+5) = 0$, so $x = 2$ or $x = -5$.
Split the middle term as $5x - 2x$; the two numbers must multiply to $-10$ and add to $+3$. Setting each factor to zero gives the roots directly. Always verify: $4 + 6 - 10 = 0$ ✓ and $25 - 15 - 10 = 0$ ✓.