Mathematics 2019 JAMB Past Questions - Question 29: At what point does the straight line y =2x +1 intersect the curve y = 2x2 + 5x -1A. (-2, -3) and (1/2,2) B. (-1/2, 0) and (2, 5) C. (1/2,2) and (1 ,3) D.(1,3) and (2,5)

Correct Answer

A

Explanation

To find the points of intersection between the straight line \(y = 2x + 1\) and the curve \(y = 2x^2 + 5x - 1\), we need to solve the system of equations formed by setting the two expressions for \(y\) equal to each other.So, we have:\[2x + 1 = 2x^2 + 5x - 1\]Rearranging this equation gives us:\[2x^2 + 3x - 2 = 0\]We can solve this quadratic equation to find the x-coordinates of the points of intersection. The solutions to this equation are \(x = -2\) and \(x = 1/2\).Substituting these values back into the equation \(y = 2x + 1\) gives us the corresponding y-coordinates:When \(x = -2\), \(y = 2(-2) + 1 = -3\), so one point of intersection is \((-2, -3)\).When \(x = 1/2\), \(y = 2(1/2) + 1 = 2\), so the other point of intersection is \((1/2, 2)\).Therefore, the correct answer is A. \((-2, -3)\) and \((1/2, 2)\).