Consider the quadratic polynomial 2x2+3x−6.
(i) Solve 2x2+3x−6=0 and denote its zeros by α and β.
(ii) Write 2x2+3x−6 as 2(x−α)(x−β).
(iii) Expand the expression obtained in part (ii) to confirm that it is identical to the original polynomial.
(iv) Find the value of the polynomial at x=α+β.