Question

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

Answer 1

Since 𝛼 + 𝛽 are the zeroes of the polynomial: 𝑥2 − 𝑥 − 4

Sum of the roots (α + β) = 1

Product of the roots (αβ) = −4

`1/alpha+1/beta-alphabeta`

`=(alpha+beta)/(alphabeta)-alphabeta`

`=(1/-4)+4=(-1/4)+4=(-1+16)/4=15/4`