MTH1101 Algebra Assignment part 3 [20 marks equivalent to 5%] The fourth and tenth terms of an arithmetic progression are defined by 4=7+8 10=19+14 a) Determine expressions for the first term and the common difference. [4] b) If the sum of the first fifteen terms of this progression is 630, find the value of the thirtieth term. [6] Let and be the roots of the quadratic equation, 2++=0. c) Prove that the roots satisfy the relations: +=; = [4] d) Given that the sum and product of roots of a quadratic equation are 16 and13, determine the equation as well as the roots. [4] Overall presentation and formatting of the assignment [2]