Find the value of the polynomial 5x – 4x 2 + 3 at
(i) x = 0 (ii) x = –1 (iii) x = 2
(i) p(x) = 5x - 4x2 + 3
= p(0) = 5(0) - 4(0)2 + 3
= 3
(ii) p(x) = 5x - 4x2 + 3 = p(-1)
= 5(-1) - 4 (-1)2 + 3
= -5 - 4 (1) + 3
= -6
(iii) p(x) = 5x - 4x2 + 3
= p(2) = 5(2) - 4(2)2 + 3
= 10 - 16 + 3 = -3
Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Fig. 9.27). Prove that ∠ACP = ∠ QCD

ABCD is a trapezium in which AB || CD and AD = BC (see Fig. 8.14). Show that
(i) ∠A = ∠B
(ii) ∠C = ∠D
(iii) ∆ABC ≅ ∠∆BAD
(iv) diagonal AC = diagonal BD [Hint : Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]

(i) The kind of person the doctor is (money, possessions)
(ii) The kind of person he wants to be (appearance, ambition)