Algebra

Rational Root Theorem

Rational Root Theorem: Level 2 Challenges

         

How many rational roots does x1000x500+x100+x+1=0{ x }^{ 1000 }-{ x }^{ 500 }+{ x }^{ 100 }+x+1=0 have?

Find the sum of all real roots of

 27x3+21x+8=0\ 27x^3+21x+8 = 0

Given that pp and qq are both prime, which of the following answer choices is true about the equation px2qx+q=0?px^{ 2 }-qx+q=0?

The polynomial x33x2+12x+16 x^3 - 3x^2 + 12x + 16 has one real root r r and two complex roots w w and z. z. What is the value of r+log2(w6+z6) r+ \log_2 \left(w^6 + z^6 \right) ?

Two of the roots of the equation ax3+bx2+cx+d=0ax^3 + bx^2 + cx + d = 0 are 232 - \sqrt{3} and 55, where a,b,c,da,b,c,d are rational numbers. If the third one is m+nm + \sqrt{n} for some integers mm and nn, find m+nm + n

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