If `alpha,beta " are the roots of the equation " ax^(2) +bx+ c=0," then what is the value of " (aalpha+b)^(-1)+(abeta+b)^(-1)`?

Options

A. `a//(bc)`
B. `b//ac`
C. `-b//(ac)`
D. `-a//(bc)`

Answer

B

Explanation

Since , `alpha and beta " are the roots of the equation " ax^(2) + bx+ c = 0,` then,
Sum of the roots , `alpha + beta =-b/a` and Product of the roots,
`alphabeta = c/a`
The expression, `(aalpha +b)^(-1) + (abeta+b)^(-1)`
` 1/(aalpha+b)+1/(abeta+b) =(alphabeta+b+ aalpha + b)/((aalpha + b)(abeta+b))`
` (a(alpha+beta)+ 2b)/(a^(2)alphabeta +ab(alpha+beta)+b^(2))`
` (a(-b//a)+2b)/(a^(2) (c//a) + ab(-b//a)+b^(2))=(-b+2b)/(ac-b^(2) + b^(2))=b/(ac)`