Question

If alpha and beta are the zeroes of the quadratic polynomial f(x)=xsquare +x-2
find the value of 1/alpha-1/beta....

Answer 1

given
f(x)=x²+x-2 and alpha and beta are the zeroes of this equation
so we have to find
$\frac{1}{ \alpha } - \frac{1}{ \beta }$
so first we have to factorise the equation.
x²+2x-1x-2
x(x+2)-1(x+2)
(x-1)(x+2)
x=1:x=(-2)
so ã=1 and ß=(-2)

$\frac{ \beta - \alpha }{ \alpha \beta } = \frac{( - \alpha) + \beta }{ \alpha \beta } = \frac{ - 1 + ( - 2)}{1 \times ( - 2)} = \frac{( - 3)}{ - 2} = \frac{3}{2}$
I hope it works