Question

α and β are zeroes of a quadratic polynomial px² + qx + 1. Form a quadratic polynomial whose zeroes are `2/α` and `2/β`.

Answer 1

α and β are zeroes of a quadratic polynomial px² + qx + 1.

α + β = `(-q)/p`

α.β = `1/p`

Quadratic equation whose roots are `2/α` and `2/β`.

`x^2 - (2/α + 2/β)x + 2/α xx 2/β`

= `x^2 - 2x(1/α + 1/β)x + 4/(αβ)`

= `x^2 - 2x((α + β)/(αβ)) + 4/(αβ)`

= `x^2 - 2x(((-9)/p)/(1/p)) + (4/1)/(p)`

= x² + 2qx + 4p

This is the required quadratic polynomial.