Question

If the answers to a quadratic equation were 2+6√3 and 2-6√3, then what was the original polynomial

Answer 1

`p(x) = k[ x^2-4x-104]`

Explanation:

Say if alpha and beta are the zeroes of the quadratic polynomial then the quadratic polynomial is given by ,

`\implies p(x) = k[x^2-(\alpha+ \beta)x +\alpha\beta ]`

• where k is a constant

`\implies p(x) = k[ x^2 - [ (2+6\sqrt3)+(2-6\sqrt3)x] + \{ (2+6\sqrt3)(2-6\sqrt3)\} ] \\\\\implies p(x) = k[ x^2 - 4x + \{ (2)^2-(6\sqrt3)^2\}] \\\\\implies p(x) = k[ x^2 -4x \{ 4-108\} ] \\\\\implies\boxed{\boxed{ p(x) = k[ x^2-4x-104] }}`

This is the required answer !