(i) Define a zero (root) of a polynomial.
(ii) Let p(x)=ax2+bx+c with a=0 and zeros α and β. Show that
(a) α+β can be written only in terms of the coefficients a and b, and
(b) αβ can be written only in terms of the coefficients a and c.
Write each expression you obtain in its simplest form, clearly indicating every algebraic step.
(iii) Using the results of part (ii), calculate the sum and the product of the zeros of the polynomial 5x2−3x+1.