Consider two real numbers α and β such that α+β=7 and αβ=10.
(i) State the relationship between the zeros and the coefficients of a quadratic polynomial ax2+bx+c whose zeros are α and β.
(ii) Explain briefly why every quadratic polynomial having α and β as its zeros must be a non-zero constant multiple of a single minimal (monic) polynomial.
(iii) Using your explanation in part (ii), write any two distinct quadratic polynomials whose zeros are α and β, and verify that the ratio of their corresponding coefficients is the same non-zero constant.