Question

If 𝛼 and 𝛽 are the zeros of the quadratic polynomial f(x) = x² − 5x + 4, find the value of `1/alpha+1/beta-2alphabeta`

Answer 1

Since 𝛼 𝑎𝑛𝑑 𝛽 are the roots of the quadratic polynomial

f(x) = 𝑥² − 5𝑥 + 4

Sum of roots = α + β = 5

Product of roots = αβ = 4

`1/alpha+1/beta-2alphabeta=(beta+alpha)/(alphabeta)-2alphabeta=5/4-2xx4=5/4-8=(-27)/4`