x^4-x^3-2x^2-x-1

This solution giao dịch with finding the roots (zeroes) of polynomials.

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Step by Step Solution

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Step 1 :

Equation at the over of step 1 : ((((x4)-(x3))-2x2)-x)-1

Step 2 :

Polynomial Roots Calculator :

2.1 Find roots (zeroes) of : F(x) = x4-x3-2x2-x-1Polynomial Roots Calculator is a phối of methods aimed at finding values ofxfor which F(x)=0 Rational Roots demo 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 integersThe Rational Root Theorem states that if a polynomial zeroes for a rational numberP/Q then p. Is a factor of the Trailing Constant and Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 1 và the Trailing Constant is -1. The factor(s) are: of the Leading Coefficient : 1of the Trailing Constant : 1 Let us demo ....

PQP/QF(P/Q)Divisor
-11 -1.00 0.00x+1
11 1.00 -4.00

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p cảnh báo that q and p.

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Originate from P/Q reduced khổng lồ its lowest terms In our case this means that x4-x3-2x2-x-1can be divided with x+1

Polynomial Long Division :

2.2 Polynomial Long Division Dividing : x4-x3-2x2-x-1("Dividend") By:x+1("Divisor")

dividendx4-x3-2x2-x-1
-divisor* x3x4+x3
remainder-2x3-2x2-x-1
-divisor* -2x2-2x3-2x2
remainder-x-1
-divisor* 0x1
remainder-x-1
-divisor* -x0-x-1
remainder0

Quotient : x3-2x2-1 Remainder: 0

Polynomial Roots Calculator :

2.3 Find roots (zeroes) of : F(x) = x3-2x2-1See theory in step 2.1 In this case, the Leading Coefficient is 1 and the Trailing Constant is -1. The factor(s) are: of the Leading Coefficient : 1of the Trailing Constant : 1 Let us thử nghiệm ....

PQP/QF(P/Q)Divisor
-11 -1.00 -4.00
11 1.00 -2.00

Polynomial Roots Calculator found no rational roots