(a) Prove that, if the zeroes of the quadratic polynomial ax2+bx+c are rational numbers, then the discriminant b2−4ac must be a perfect square.
(b) Using the result proved in part (a), or otherwise, obtain the complete factorisation of 7x2−22x+3 over the set of rational numbers.
(c) Verify your answer to part (b) by showing that each factor yields zero when substituted into the original polynomial.