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Let $ f:(-1,1) \rightarrow \mathbb{R}$ be the function defined by $f(x)=x^2e^{1/(1-x^2)}$. Then

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List Question

Convex function and unique zero

Solving a radical equation

Proving an inequality for the solution of a quadratic equation

Let $ f:(-1,1) \rightarrow \mathbb{R}$ be the function defined by $f(x)=x^2e^{1/(1-x^2)}$. Then

Solve for x: $(x^2-3x+1)^2-3(x^2-3x+1)+1=x$

To solve a 7th-degree polynomial arising from a geometric progression

Pattern Search method for roots

Using expansion of $\sin8\theta$ to find equation with given roots

Solve in $\mathbb{R}$ the equation : $x^4+x-4=0$

The application of Rouche's theorem

Math Competition Question - Algebra

Given $f(x)$ and $g(x)$, find the positive difference between the respective sums of their roots.

What are the linear factors of $x^3 - 2$?

The polynomial has a root in the interval $(a_1,a_1+1).$

Distinct roots of $ax^2-bx+c=0$ in $(0,1)$, where $a,b,c\in \mathbb{Z}^+$

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