The equation formed by multiplying each root of `ax^(2) + bx+ c = 0" by "2 " is "x^(2) = 36x + 24 =0`
If `alpha and beta` are the roots of the equation `x^(2) + bx + c = 0` , then what is the value of `alpha^(-1) + beta^(-1)`?

Options

A. `-b/c`
B. `b/c`
C. `c/b`
D. `-c/b`

Answer

A

Explanation

Consider `alpha^(-1) +beta^(-1) = 1/alpha + 1/beta = (alpha+beta)/(alpha beta)`
Equation is `x^(2) + bx + c = 0 `
Now, sum of roots `= alpha + beta = - b`
and prosuct of roots ` = alpha. beta = c `
` :. (alpha + beta)/(alpha beta) = - b/c `
Hence, ` alpha^(-1) + beta^(-1) = -b/c`