A polynomial is identically equal to zero if and only if all of its coefficients are equal to zero. eg. The power series on the left is identically equal to zero, consequently all of its coefficients are equal to 0:
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The definite integral of any function identically equal to zero between any two points is zero. Integral is the area under the graph of the given function. Sometimes the terms "integral" or "indefinite integral" are used to refer to the general antiderivative of a function, especially in many textbooks. In this case, the indefinite integral is equal to an arbitrary constant, and it is important to distinguish between these two cases.
No.
set the values of the y equal to zero
A value of the variable that makes the polynomial equal to zero (apex)
when you have a function lets say y = mx + b then you set it equal to zero and solve you are finding the x values that give you a y value of zero and a y value of zero lies on the x-axis. therefore when you find a zero of a function it's really the x value of where the function touches or crosses the x axis. hope this helps