Theory question 109
Algebraic Expressions(a) Simplify (x + 2)/(x − 2) − (x + 3)/(x − 1)
(b) The graph of the equation y = Ax2 + Bx + C passes through the points (0, 0), (1, 4) and (2, 10). Find the: (i) value of C; (ii) values of A and B; (iii) co-ordinates of the other point where the graph cuts the x-axis.
Show the model answer
Model answer
(a) [(x + 2)(x − 1) − (x + 3)(x − 2)]/[(x − 2)(x − 1)] = [(x2 + x − 2) − (x2 + x − 6)]/[(x − 2)(x − 1)] = 4/[(x − 2)(x − 1)].
(b)(i) (0, 0): C = 0.
(ii) A + B = 4 and 4A + 2B = 10 → 2A = 2 → A = 1, B = 3.
(iii) y = x2 + 3x = x(x + 3) = 0 → the other point is (−3, 0).
Explanation
Substitute each point into the equation to get simultaneous equations.