Which quadratic equation has roots 3 and $-5$?

Explanation

1. 01

   Sum of roots $= 3 + (-5) = -2$; product $= 3 \times (-5) = -15$.

2. 02

   The equation is $x^2 - (\text{sum})x + \text{product} = 0$, i.e. $x^2 - (-2)x - 15 = 0$.

3. 03

   So $x^2 + 2x - 15 = 0$. Check: $(x - 3)(x + 5)$ expands to this.