At what points does the straight line y = 2x + 1 intersect the curve y = \(2x^2\) + 5x - 1?
A
(-2, -3) and(\(\frac{1}{2}\), 2)
B
(1, 0), (1, 3)
C
(4, 0) and (0,1)
D
2, 0) and (0,1)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
line = y = 2x + 1, curve = y = \(2x^2\) + 5x - 1
2x + 1 = \(2x^2\) + 5x - 1
\(2x^2\) + 3x - 2 = 0
factorizing
(2x - 1)( x + 2) = 0
x = 1/2 or -2
when x = 1/2
y = 2 * 1/2 + 1 = 2 ( using the equation of a straight line )
when x = -2, y = -3
therefore, the points are ( 1/2, 2) and ( -2, -3)
Source: Myschool Past Questions Archive (Record #32156)