Question

If α and β are the zeros of the quadratic polynomial p(y) = 5y² – 7y + 1, find the value of `1/α + 1/β`.

Answer 1

Since α and β are the zeroes of the polynomials

p(y) = 5y² – 7y + 1

Sum of the zeroes `alpha+beta="-coeeficient of x"/("coefficient of "x^2)`

`=-(-7)/5`

`=7/5`

Product of zeroes `=alphabeta="constant term"/"coefficient of "x^2`

`=1/5`

We have, `1/alpha+1/beta=(alpha+beta)/(alphabeta)`

By substituting `alpha+beta=7/5` and `alphabeta=1/5` we get,

`1/alpha+1/beta=(7/5)/(1/5)`

`1/alpha+1/beta=7/5xx5/1`

`1/alpha+1/beta=7`

Hence, the value of `1/alpha+1/beta` is 7.