Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  81 +  24k2

Step  2  :

Polynomial Roots Calculator :

 2.1    Find roots (zeroes) of :       F(k) = 16k²+81
Polynomial Roots Calculator is a set of methods aimed at finding values of  k  for which   F(k)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  k  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  16  and the Trailing Constant is  81.

 The factor(s) are:

of the Leading Coefficient :  1,2 ,4 ,8 ,16
 of the Trailing Constant :  1 ,3 ,9 ,27 ,81

 Let us test ....

Note - For tidiness, printing of 45 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Final result :

  16k2 + 81