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Rational Root Theorem

The rational root theorem describes a relationship between the roots of a polynomial and its coefficients. For a good time, use the theorem to prove that the square root of 2 is not rational.

Level 2

         

How many rational roots does \({ x }^{ 1000 }-{ x }^{ 500 }+{ x }^{ 100 }+x+1=0\) have?

Find the sum of all real roots of

\[\ 27x^3+21x+8 = 0\]

Given that \(p\) and \(q\) are prime, which of the following answer choices is true for the equation \(px^{ 2 }-qx+q=0\)?

The polynomial \[ x^3 - 3x^2 + 12x + 16 \] has one real root \( r \) and two complex roots \( w \) and \( z.\) What is the value of \( r+ \log_2 \left(w^6 + z^6 \right) \)?

Two of the roots of the equation \[ax^3 + bx^2 + cx + d = 0\] are \(2 - \sqrt{3}\) and \(5\), where \(a,b,c,d\) are rational numbers. If the third one is \(m + \sqrt{n}\) for some integers \(m\) and \(n\), find \(m + n\)

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