If p(x) = ax2 + bx + c and a + b + c = 0, then one zero is

Let's solve the problem step by step:

Step 1: Given that p(x) = ax^2 + bx + c and a + b + c = 0, we need to find one zero of the quadratic equation.

Step 2: To find the zero of the quadratic equation, we set p(x) equal to zero and solve for x. So, we have ax^2 + bx + c = 0.

Step 3: Since a + b + c = 0, we can substitute -c for a + b in the equation. This gives us -c + bx + c = 0.

Step 4: Simplifying the equation, we get bx = 0.

Step 5: Dividing both sides of the equation by b, we have x = 0.

Step 6: Therefore, the zero of the quadratic equation p(x) = ax^2 + bx + c, where a + b + c = 0, is x = 0.

In conclusion, one zero of the quadratic equation is x = 0.