Maths F4...4

126(a) Sum of roots = -3m/10; Product of roots = 2/10 = 1/5
Hence -3m/10 - 1/5 = 7/10 => m = -3
(b) 10x^2 + 3(-3)x + 2 = 0
10x^2 - 9x + 2 = 0
(2x - 1)(5x - 2) = 0
x = 1/2 or x = 2/5

35(a) y = k/x^2, where k is a non-zero constant.
Sub. y = a and x = 3, a = k/9 => k = 9a
Sub. y = b and x = 5, b = k/25 => k = 25b
Hence 9a = 25b
a/b = 25/9
a:b = 25:9
(b) Sub. y = 27/5 and x = 25/9,
27/5 = k/(25/9)^2
k = 125/3
Variation constant = 125/3