A quadratic polynomial has leading coefficient 3 and its zeros satisfy the relationship: one zero is exactly twice the other. Further, the sum of its zeros is 35.
(i) Let the two zeros be α and 2α. Using the given information, determine the value of α.
(ii) Hence write the quadratic polynomial in the form 3x2+bx+c.
(iii) Find the product of the zeros from your polynomial and verify that it coincides with the value obtained directly from the constant term and leading coefficient.
(iv) Evaluate the polynomial at x=1 and interpret the sign of this value with respect to the graph of the polynomial.