Question

Solve the equation 6x^4-35x^3+62x^2-35x+6

Answer 1

Answer:

Find roots (zeroes) of : F(x) = 6x4-35x3+62x2-35x+6

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 6 and the Trailing Constant is 6.

The factor(s) are:

of the Leading Coefficient : 1,2 ,3 ,6

of the Trailing Constant : 1 ,2 ,3 ,6

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 144.00

-1 2 -0.50 43.75

-1 3 -0.33 25.93

-1 6 -0.17 13.72

-2 1 -2.00 700.00

-2 3 -0.67 68.44

-3 1 -3.00 2100.00

-3 2 -1.50 346.50

-6 1 -6.00 17784.00

1 1 1.00 4.00

1 2 0.50 0.00 2x-1

1 3 0.33 0.00 3x-1

1 6 0.17 1.73

2 1 2.00 0.00 x-2

2 3 0.67 1.04

3 1 3.00 0.00 x-3

3 2 1.50 5.25

6 1 6.00 2244.00

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that

6x4-35x3+62x2-35x+6

can be divided by 4 different polynomials,including by x-3

Step-by-step explanation:

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