Explanation:
STEP
1
:
Equation at the end of step 1
2^2 k^4 + 1
STEP
2
:
Polynomial Roots Calculator :
2.1 Find roots (zeroes) of : F(k) = 4k4+1
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 4 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 5.00
-1 2 -0.50 1.25
-1 4 -0.25 1.02
1 1 1.00 5.00
1 2 0.50 1.25
1 4 0.25 1.02
Polynomial Roots Calculator found no rational roots
Final result :
4k4 + 1