Math CentralQuandaries & Queries


Question from deciree, a student:

How could i get the value of x with this equation:

Thank you!

Hi Deciree,

I would first multiply both sides by 13 × 2 to eliminate the fractional coefficients and obtain the equivalent equation

2x3 + 24x - 13 = 0.

Since the equation now has integer coefficients I can use the Rational root theorem. Thus if p and q are integers and p/q is in lowest terms and is a root of the equation then p divides 13 and q divides 2. Thus

p is ±1 or ±13 and q is ±1 or ±2.

Construct the 8 possible roots p/q and test if any of them is a root.


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