If $3.5 - {\sqrt 2}$ and $3.5 + {\sqrt 2}$ are the roots of a quadratic equation ${ax^2 + bx + c = 0}$; then which of the following is not correct?

A. a is nonzero - I ruled out this because if was 0 then it wouldn't be a quadratic equation anymore
B. discriminant is positive - There are two solutions
C. a, b, and c are all real or all complex - I'm not sure but I had a feeling this was correct to, since the roots were all real numbers. Is this correct?

How would I choose between D or E?
D. $\frac{b}{a}$ and $\frac{c}{a}$ must be both rational
E. $\frac{b}{a}$ and $\frac{c}{a}$ must be both integral

Website on solution: http://www.mathsisfun.com/algebra/polynomials-sums-products-roots.html

• I have to say that I find C confusing - I think they must mean "all of them are real or none of them are real" since real numbers are complex numbers. – Mark Bennet Apr 26 '14 at 13:08

Using Vieta's formula $$-\frac ba=3.5-\sqrt2+3.5+\sqrt2=7$$
and $$\frac ca=(3.5-\sqrt2)(3.5+\sqrt2)=(3.5)^2-2=\frac{41}4$$