If `alpha` and `beta` are the roots of the equation `ax^2+bx+c=0` where `alpha` 0 then (a`alpha`+b)(a`beta`+b) is equal to

Options

A. `ab`
B. `bc`
C. `ca`
D. `abc`

Answer

C

Explanation

Given equation `ax^(2) + bx + c=0" "(where a != 0)`
`alpha and beta " are roots of given equation" `
` (a alpha+ b) (a beta +b) = a^(2) alpha beta + a b alpha + ab beta + ba^(2)`
Form the given quadratic equation
` alpha + beta = (-b)/a , alpha beta = c/a`
` a^(2) xxc/a + ab xx -b/c + b^(2) = ac`