A cubic polynomial with integer coefficients has and as its zeros

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

A cubic polynomial with integer coefficients has

2+\sqrt{3}

and

-1

as its zeros. (i) Write all the zeros of the polynomial, giving reasons. (ii) Construct the polynomial in standard form with leading coefficient

1

. (iii) Factorise the polynomial completely.