Question

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

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=(beta-alpha)/(alphabeta)=(-(alpha-beta))/(alphabeta)`   ................(i)

From (i) we know that  `alpha - beta = sqrt(b^2-4ac)/(2a)`

αβ = `c/a`

Putting the values in the (a) `=-((sqrtb^2-4acxxa)/(axxc))=(-sqrt(b^2-4ac))/c`