Mathematics

Problem

Let the quadratic polynomial be

r(x)=6x^{2}-13x+6

. a. (i) Factorise

r(x)

and hence find its zeros

\alpha

and

\beta

. b. (ii) Verify by direct substitution that each zero satisfies

r(x)=0

. c. (iii) Form a new quadratic polynomial whose zeros are

\alpha^{2}

and

\beta^{2}

, and express it in standard form

Ax^{2}+Bx+C

with integer coefficients.