to identify the graph of a polynomial whose both zeros are positive. Zeros of a polynomial are the x-intercepts of its graph. For both zeros to be positive, the graph must intersect the positive x-axi

Step 1: Analyze Question 1. The question asks to identify the graph of a polynomial whose both zeros are positive. Zeros of a polynomial are the x-intercepts of its graph. For both zeros to be positive, the graph must intersect the positive x-axis at two distinct points. Graph (a) shows one zero at x=0 and another positive zero. This does not represent two positive zeros. Graph (b) is a circle, not a polynomial graph. Graph (c) shows a parabola intersecting the x-axis at two points, both of which are on the positive side of the x-axis. This means both zeros are positive. Graph (d) shows one negative zero and one positive zero. Therefore, graph (c) represents a polynomial with two positive zeros. The final answer is c. Step 2: Analyze Question 2. The question asks for the nature of the solution to the system of equations x=2 and x=3. For a system of equations to have a solution, there must be a value (or set of values) that satisfies all equations simultaneously. Here, we have two conditions for x: 1. x=2 2. x=3 It is impossible for x to be equal to 2 and 3 at the same time. Therefore, there is no value of x that can satisfy both equations. The final answer is c. Step 3: Analyze Question 3. The question states that the numbers 1-a, 3-a, and 5-a are in an arithmetic progression (AP) and asks for the common difference. In an arithmetic progression, the common difference (d) is the difference between any term and its preceding term. Let the terms be t_1 = 1-a, t_2 = 3-a, and t_3 = 5-a. Calculate the common difference using the first two terms: d = t_2 - t_1 d = (3-a) - (1-a) d = 3 - a - 1 + a d = 2 Verify the common difference using the second and third terms: d = t_3 - t_2 d = (5-a) - (3-a) d = 5 - a - 3 + a d = 2 Both calculations yield the same common difference, which is 2. The final answer is c.