Question

if alpha and beta are zeroes of a polynomial x²+x-2. find the value of 1/alpha - 1/beta​

Answer 1

Step-by-step explanation:

${x}^{2} + x - 2 = 0\\ {x}^{2} + 2x - x - 2 = 0 \\ x(x + 2) - 1(x + 2) = 0 \\ (x + 2)(x - 1) = 0 \\ x + 2 = 0 \: \: \: \: \: \: x - 1 = 0 \\ x = - 2 \: \: \: \: \: x = 1 \\ \\ \alpha = - 2 \: \: \: \: \: \beta = 1$

$\frac{1}{ \alpha } - \frac{1}{ \beta } \\ = \frac{1}{ - 2} - \frac{1}{1} \\ = \frac{1}{ - 2} - 1 \\ = \frac{ - 1 - 2}{2} \\ = - \frac{3}{2}$

Hope you get your answer