Question

how many real and non - real solutions does the graphed equation have? (1 point) two real and one non - real zero real and three non - real three real and zero non - real one real and one non - real

Explanation:

Step1: Identify x-intercepts

The graph intersects the x - axis at \(x=-1\), \(x = 0\), and \(x = 1\). These are the real solutions of the equation (since the x - intercepts of the graph of a function \(y = f(x)\) correspond to the real solutions of the equation \(f(x)=0\)).

Step2: Determine the degree and non - real solutions

For a polynomial function, the number of solutions (real and non - real) is equal to its degree (by the Fundamental Theorem of Algebra). The graph shown has three x - intercepts, so it is at least a cubic (degree 3) polynomial. A cubic polynomial has exactly 3 solutions (counting multiplicities) in the complex number system. Since we have 3 real solutions, the number of non - real solutions is \(3 - 3=0\).

Answer:

three real and zero non - real (corresponding to the option "three real and zero non - real")