The polynomial \(p(x)\) is defined by \[p(x)=x^4-10x^3+20x^2-30x+40.\]

(a) Find the quotient when \(p(x)\) is divided by \((x^2+3)\) and show that the remainder is \(-11\). [3]

(b) Hence find the real roots of the equation \(p(x)+11=0\), giving your answers in exact form. [3]