Given that, the roots of the quadratic equation are 3 and -1. Let \( \Large \alpha = 3 \ and \ \beta = -1 \) Sum of roots = \( \Large \alpha + \beta = 3 - 1 = 2 \) Product of roots = \( \Large \alpha . \beta = \left(3\right) \left(-1\right) = -3 \) Therefore, Required quadratic equation is \( \Large x^{2} - \left( \alpha + \beta \right) x + \alpha \beta = 0 \) \( \Large x^{2} - \left(2\right)x + \left(-3\right) = 0 \)
\( \Large x^{2} - 2x - 3 = 0 \)