The line y = 2x + 1 intersects the parabola y = 3x ^ 2 + x-1 at two points. Calculate the coordinates

The line y = 2x + 1 intersects the parabola y = 3x ^ 2 + x-1 at two points. Calculate the coordinates of the point in the larger abscissa.

The coordinates of the intersection points of the graphs of the two functions are numbers that satisfy the conditions of both the first and second functions. Therefore, we get:

3 * x² + x – 1 = 2 * x + 1,

3 * x² + x – 1 – 2 * x – 1 = 0,

3 * x² – x – 2 = 0.

Let’s solve the resulting quadratic equation and for this we find its discriminant:

D = (-1) ² – 4 * 3 * (-2) = 1 + 24 = 25.

So x = (1 + 5) / 6 = 1 and x = (1 – 5) / 6 = -2 / 3.

Of these two roots, x = 1 is the largest, that is, it is the large abscissa of the intersection points.

The ordinate of this point will be: y = 2 * 1 + 1 = 3 * 1² + 1 – 1 = 3.

Answer: (1; 3).