Question

If `alpha` and `beta` are the zeroes of the quadratic polynomial `x^2 +5x+6` find a quadratic polynomial whose zeroes are `1/ alpha` and `1/ beta?`

Answer 1

`6x^2+5x+1`

Explanation:

Given:

`ax^2+bx+c" "` with `a != 0` and `c != 0`

Then:

`1/x^2(ax^2+bx+c) = c(1/x)^2+b(1/x)+a`

So the zeros of `ax^2+bx+c` are the reciprocals of the zeros of `cx^2+bx+a`

Hence a quadratic whose zeros are the reciprocals of the zeros of:

`x^2+5x+6`

is:

`6x^2+5x+1`