Question

solve x^4 - 5x^3 +7x^2- 5x +1=0 ?

Answer 1

Answer: x ≓ 0.301521301

Step-by-step explanation:

x^4-5x^3+7x^2-5x+1=0  

One solution was found :

                        x ≓ 0.301521301

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  2 more similar replacement(s).

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((((x4)-(5•(x3)))+7x2)-5x)+1  = 0  

Step  2  :

Equation at the end of step  2  :

 ((((x4) -  5x3) +  7x2) -  5x) +  1  = 0  

Step  3  :

Polynomial Roots Calculator :

3.1    Find roots (zeroes) of :       F(x) = x4-5x3+7x2-5x+1

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  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  1  and the Trailing Constant is  1.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        19.00      

     1       1        1.00        -1.00