Algebra question?

Question

Find a polynomial with real coefficients and least degree having the given zeroes:

-2 + radical 5, -2- radical 5, -2, 1

I'm trying to finish my math review for finals and we haven't learned this yet. So frustrating, please help!

Answer 1

Greetings,

Recall that if r is a zero of the polynomial then (x - r) is a factor of the polynomial

So multiply the factors given by the 4 roots to get the polynomial

(x - [-2 - sqrt5]) (x - [-2 + sqrt5])(x + 2)(x - 1)

= (x^2 + 4x - 1)(x^2 + x - 2)
= x^4 + 5x^3 + x^2 - 9x + 2

Regards

Answer 2

(x+2)(x-1)(x+2-sqrt(5))(x+2+sqrt(5))
Now just multiply tis out and you have your answer