Write a polynomial with these roots 1 2 square root of 3 2

Write a polynomial with these roots.

-1

2 + square root of 3

2 - square root of 3

So, -1 = (x+1)

How do you find the quadratic working backwards from roots?

Solution

Roots : x=-1 ---- (x+1) factor

x= 2+sqrt3 ----- (x-2 -sqrt3)

; x= 2- sqrt3 ------ (x-2 +sqrt3)

quadratic function from the above complex roots:

(x-2 -sqrt3)(x-2 +sqrt3) = (x^2 -2x +xsqrt3 + -2sqrt3 -2x +4 -2sqrt3 -sqrt3*x +2sqrt3 -3)

=(x^2 -4x +1)

So, f(x) = (x+1)(x^2 -4x+1)

So, polynomial f(x) =