Question

You can use a system of equations to graph and solve the polynomial equation 3 x cubed + x = 2 x squared + 1. Which statement is true? The system has one solution, and the equation has three zeroes. The y-coordinates of the solutions to the system and the zeroes of the equation are not equal. The x-coordinates of the solutions to the system and the zeroes of the equation are not equal. The equation has one zero, and the system has three solutions.

Answer 1

The equation has one zero, and the system has three solutions ( 1 real and 2 complex solutions).

Solution of the polynomial equation

The solution of the polynomial equation is determined as follows;

3x³ + x = 2x² + 1

3x³ - 2x² + x - 1 = 0

$3(x - \frac{2}{9} )^3+ \frac{5}{9} (x - \frac{2}{9} )- \frac{205}{243} = 0\\\\x = 0.78 \ (one \ real \ solution)\\\\x = -0.058-0.65i\\\\x = -0.058+0.65i \ \ (2 \ complex \ solutions)$

Thus, we can conclude that the equation has one zero (real solution), and the system has three solutions ( 1 real and 2 complex solutions).

Learn more about polynomial equations here: brainly.com/question/2833285

#SPJ1