Question 6
(a) The sum of two numbers is 91. If one-quarter of one of the numbers added to one- fifth of the other is 21, find the numbers.
(b) If are the roots of the quadratic equation , find the values of , and .
Observation
The Chief Examiner reported that majority of the candidates’ who attempted this question got it right. However, some candidates who attempted part (b) mixed up the signs when forming the quadratic equation and when comparing it with the given equation.
In part (a), they were expected to assign x and y as the numbers.
The first sentence gives x + y = 91 __________ (1).
The second sentence gives x + . Simplifying gives 5x + 4y = 420 ________ (2). Solving the two equations gives x = 5 and y = 35. Therefore, the numbers are 35 and 56.
In part (b), they were expected to form linear equation using the roots as shown:
(x – 2). Simplifying gives 8x2 – 11x – 10 = 0. By comparing the equation with gives p = 8, q = – 11, r = – 10.