List questions from roots

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Does this characteristic polynomial has a root of multiplicity 2?

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show this equation has $m-1$ distinct real roots

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root of bijective function

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Finding the roots, with multiplicity, of a polynomial with compound angle formula

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Find a real cubic polynomial whose has roots $1$ and $i$.

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How one can show that this seven degree polynomial has no real roots in $(0,1)$?

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Stating that either root is zero in solving a quadratic equation

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Find equation roots

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Rouche’s theorem Application right half plane

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If $ \alpha_i, i=0,1,2...n-1 $ be the nth roots of unity, the $\sum_{i=0}^{n-1} \frac{\alpha_i}{3- \alpha_i}$ is equal to?

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Solve for $x$ : $x^4 = 5(x-1)(x^2 - x +1)$

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Quadratic equation of graphs

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Possible values of a parameter in an arithmetic progression

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List Question

Real Analysis - Assessing the number of zeros

Does this characteristic polynomial has a root of multiplicity 2?

show this equation has $m-1$ distinct real roots

root of bijective function

Finding the roots, with multiplicity, of a polynomial with compound angle formula

Find a real cubic polynomial whose has roots $1$ and $i$.

Quadratic equation - arithmetic progression

How one can show that this seven degree polynomial has no real roots in $(0,1)$?

Stating that either root is zero in solving a quadratic equation

Find equation roots

Rouche’s theorem Application right half plane

If $ \alpha_i, i=0,1,2...n-1 $ be the nth roots of unity, the $\sum_{i=0}^{n-1} \frac{\alpha_i}{3- \alpha_i}$ is equal to?

Solve for $x$ : $x^4 = 5(x-1)(x^2 - x +1)$

Quadratic equation of graphs

Possible values of a parameter in an arithmetic progression

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