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Question 12
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(a) The polynomial f(x) = 2x3 + Px + qx + r is divisible by (2x2 – 7x + 3). It has a remainder of -36 when it is divided by (x + 1). Find the
(i) values of constants P, q and r;
(ii) zeroes of f(x)
- Find the truth set of x2 – 3x + 2 < 0.
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- Two linear transformations are defined by
P:(x,y) (-2 + 3y, 5x – 4y)
T:(x,y) (-3x – 4y, 6x – 5y)
Find the
- inverse of T;
- image of (1,3) under the transformation P.
- Find the volume, in terms of p, of the solid formed when the area enclosed by the lines y = 1, 2y = x + 1 and x = 0 is rotated through two right angles about the y – axis.
Very few candidates reportedly attempted this question and they performed poorly. The matrix of transformation T = .
= 15 + 24 = 39. T-1 = . Therefore, required inverse T-1 (x, y) = =
(ii) P = . Therefore the image of (1,3) under P = = = (7, -7).
For part (b), since the volume generated was half of the total volume, the formular becomes V = . 2y = x + 1. Hence x = 2y – 1. When x = 0, y = ½ and when y = 1, x = 1. Thus, V = = = cubic units. |
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