Find the abscissas of the intersection points of the graphs of the functions y = 4x² + x and y = 2-4x-3x².

Y = 4 * X ^ 2 + X.

Y = 2 – 4 * X – 3 * X ^ 2.

Let’s equate both equations and solve it.

4 * X ^ 2 + X = 2 – 4 * X – 3 * X ^ 2.

4 * X ^ 2 + 3 * X ^ 2 + 4 * X + X – 2 = 0.

7 * X ^ 2 + 5 * X – 2 = 0.

Let’s solve the quadratic equation.

D = b ^ 2 – 4 * a * c = 5 ^ 2 – 4 * 7 * (-2) = 25 + 56 = 81.

X1 = (-5 – √81) / (2 * 7) = (-5 – 9) / 14 = -14 / 14 = -1.

X2 = (-5 + √81) / (2 * 7) = (-5 + 9) / 14 = 4/14 = 2/7.

Answer: The abscissas of the intersection points are -1 and 2/7.