Question

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha+1/beta-2alphabeta`

Answer 1

f(x) = ax² + bx + c

α + β = `(-b/a)`

αβ = `c/a`

since α + β are the roots (or) zeroes of the given polynomials

then

`1/alpha+1/beta-2alphabeta`

`rArr[(alpha+beta)/alphabeta]-2alphabeta`

`rArr(-b)/axxa/c-2c/b=-2c/a-b/c=(-ab-2c^2)/(ac)-[b/c+(2c)/a]`