A straight line y = mx meets the curve y = x2 - 12x + 40 in two distinct points. If one of them is (5, 5) find the other
A
(5, 6)
B
(8, 8)
C
(8, 5)
D
(7,7)
E
(7, 5)
Verified Correct Answer: E.
Step-by-Step Mathematical Solution
When y = 5, y = x2 - 12x + 40, becomes
x2 - 12x + 40 = 5
x2 - 12x + 40 - 5 = 0
x2 + 12x + 35 = 0
x2 - 7x - 5x + 35 = 0
x(x - 7) - 5(x - 7) = 0
= (x - 5)(x - 7)
x = 5 or 7
Source: Myschool Past Questions Archive (Record #32355)