Question

If alpha and beta are zeroes of p(x)=x2+x-2, find the value of 1/alpha - 1/beta.​

Answer 1

Answer:

3 / 2  or  - 3 / 2

Step-by-step explanation:

 Polynomials written in the form of x^2 - Sx + P represent S as sum of their roots and P as product of their roots.

 Here, polynomial is x^2 - ( - 1 )x - 2.

So S = - 1 and P = - 2.

   P = αβ = - 2

S = sum of roots = - 1

   ⇒ α + β = - 1

Square on both sides:

   ⇒ ( α + β )^2 = ( - 1 )^2

   ⇒ α^2 + β^2 + 2αβ = 1

   ⇒ α^2 + β^2 + 2( - 2 ) = 1

   ⇒ α^2 + β^2 = 1 + 4

   ⇒ α^2 + β^2 = 5

   ⇒ α^2 + β^2 - 2αβ = 5 - 2αβ

   ⇒ ( β - α )^2 = 5 - 2( - 2 )

   ⇒ ( β - α )^2 = 9

   ⇒ β - α = 3 or - 3

In question,

1 / α - 1 / β

⇒ ( β - α ) / αβ

     β - α = 3 or - 3  ; αβ = - 2

⇒ ( 3 / - 2 )  or  ( - 3 / - 2 )

⇒ - 3 / 2 or 3 / 2