How to determine when a function changes sign?

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To determine when the algebraic function f(y;a) = y^4 + b*y^3 + c*y^2 + d*y + e changes sign between 0 and 1+a, one must analyze the behavior of the function over that interval. The coefficients b, c, d, and e are dependent on the parameter a, which influences the function's roots and sign changes. Evaluating the function at the endpoints, f(0;a) and f(1+a;a), is essential to identify sign changes. Additionally, applying the Intermediate Value Theorem can help establish conditions under which the function crosses the x-axis. Understanding the notation f(y;a) as a function of y with parameters influenced by a is crucial for further analysis.
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Hi all.
Say, I have an alegebric function, e.g. f(y;a)=y^4+b*y^3+c*y^2+d*y+e,
where the coefficients b,c,d and e are all depends on a single parameter, a.

What I want to do is to check what is the condition of a for the function f(y;a) to change its sign between 0 and 1+a, do you have any idea to do so?
 
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i don't understand your notation, what does f(y:a) mean?
 
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