The graph of a quadratic polynomial \(y=p(x)\) passes through the points \((-6,0)\), \((1,-14)\) and \((3,0)\).
Answer the following questions:
(i) Using the zeroes of \(p(x)\) and the point \((1,-14)\), find the polynomial \(p(x)\).
(ii) Using the zeroes obtained from the given graph of \(p(x)\) , form a quadratic polynomial \(q(x)\) whose constant term is \(36\).
(iii) If the zeroes of \(p(x)\) are \(\alpha\) and \(\beta\), obtain a quadratic polynomial \(f(x)\) whose zeroes are \(\alpha+\beta\) and \(\beta-\alpha\).
Answer variants:
\(2x^2+6x+36\)
\(x^2-6x-27\)
\(-2x^2-6x+36\)
\(x^2-3x-18\)
\(x^2+6x-27\)
\(x^2+3x-18\)