Question

If α,β are the roots of y^2-2y+3=0 then find the equation whose roots are 1/α^2 and 1/β^2 ?

Answer 1

`9y^2+2y+1=0`

Explanation:

The given quadratic equation would have sum of the roots to be `alpha +beta= 2` and product of roots to be `alpha beta=3`

It is required to form a quadratic equation whose sum of roots to be `1/alpha^2 + 1/beta^2` and product of roots to be `1/(alpha^2 beta^2)`

Using the values of `alpha` and `beta`, indicated above, the sum and product of the roots of the desired equation would be

The required quadratic would then be `y^2 +2/9 y +1/9=0` or,
`9y^2+2y+1=0`