A polymomial p(x) = ax^2 + bx + c where a, b, c are some rational, has 1 + root 3 as one of the zeros and also p (2) = - 2, Find values of a, b and c. Please work the solution. Tried it many times but still can't get the answer/ The answer is a = 1, b = -2 and c = -2.

Answer 1

ok, if a,b,c are rational, then the other root is 1-√3 and we have

p(x) = k(x-(1+√3))(x-(1-√3))
= k((x-1)^2 - 3)
= k(x^2-2x-2)

Now, p(2) = -2, so
-2 = k(-2)
k=1

p(x) = x^2-2x-2

as desired