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