Question

If the zeroes of a polynomial are 2+root3 and 2-root3 find the polynomial

Answer 1

Answer:

if a and b are the zeros of the polynomial, then we can write the polynomial as (x-a)(x-b)

= x^2 - x(a + b) + ab

here a = 2+√3 and b = 2 - √3

therefore p(x) = x^2 - x(2+√3+2-√3) + (2+√3)(2-√3)

= x^2 - x (4) + (4 - 3) [ (a+b)(a-b) = a^2 - b^2 ]

p(x) = x^2 - 4x + 1. Answer