Mathematics

Problem

(i) Define a zero (root) of a polynomial. (ii) Let

p(x)=ax^{2}+bx+c

with

a\neq0

and zeros

\alpha

and

\beta

. Show that (a)

\alpha+\beta

can be written only in terms of the coefficients

a

and

b

, and (b)

\alpha\beta

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

5x^{2}-3x+1

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