Question

If a and B are the zeroes of the polynomial 2x² + 3x - 6. then find the

value of the following (a) a-ß​

Answer 1

Answer:

$\alpha - \beta = \frac{ \sqrt{57} }{2} .$

Step-by-step explanation:

$2 {x}^{2} + 3x - 6 = 0 \\ \\ \alpha + \beta = \frac{ - 3}{2} \\ \\ \alpha \beta = \frac{ - 6}{2} = - 3 \\ \\ \\ \alpha - \beta = \sqrt{ {( \alpha + \beta )}^{2} - 4 \alpha \beta } \\ \\ = \sqrt{ \frac{9}{4} + 12} \\ \\ = \sqrt{ \frac{9 + 48}{4} } \\ \\ = \frac{ \sqrt{57} }{2} \: \: .$