Question

If α and β are the zeros of the quadratic polynomial f(x) = 2x²+3x -2 . Find the value of α - β

Answer 1

Answer:

$\alpha - \beta = \frac{ \sqrt{17} }{2} .$

Step-by-step explanation:

$2 {x}^{2} + 3x - 2 = 0. \\ \alpha + \beta = - \frac{3}{2} \\ \alpha \beta = - \frac{2}{2} = - 1 \\ \\ \alpha - \beta = \sqrt{ {( \alpha + \beta) }^{2} - 2 \alpha \beta } \\ \\ = \sqrt{ {( \frac{3}{2}) }^{2} - 2( - 1)} \\ \\ = \sqrt{ \frac{9}{4} + 2} \\ \\ = \sqrt{ \frac{9 + 8}{4} } \\ \\ = \frac{ \sqrt{17} }{2} .$