Given:
α and β are the zeros of the quadratic polynomial f(x) = x2 + x - 2
To find:
the value of \(\frac{1}{\alpha}\) - \(\frac{1}{\beta}\)
Solution:
α and β are the roots of the given equation
Sum of root:
Product of the roots:
Use
(a + b)2 = a2 + b2 + 2ab
and
(a - b)2 = a2 + b2 - 2ab
to find the value of
β - α. (β+α)2 = β2+α2+2βα
add and subtract 2βα on right hand side of the above equation.
(β+α)2=β2+α2+2βα+2βα - 2βα(β+α)2 = (β - α)2+4βα
