d3+d2+d+1 root of these equation
Answers
Answer:
d3+d2+d+1=0
This deals with linear equations with one unknown.
Overview
Steps
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3 solution(s) found
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Step by Step Solution
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Reformatting the input :
Changes made to your input should not affect the solution:
(1): "d2" was replaced by "d^2". 1 more similar replacement(s).
Step by step solution :
STEP
1
:
Checking for a perfect cube
1.1 d3+d2+d+1 is not a perfect cube
Trying to factor by pulling out :
1.2 Factoring: d3+d2+d+1
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: d+1
Group 2: d3+d2
Pull out from each group separately :
Group 1: (d+1) • (1)
Group 2: (d+1) • (d2)
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Add up the two groups :
(d+1) • (d2+1)
Which is the desired factorization
Polynomial Roots Calculator :
1.3 Find roots (zeroes) of : F(d) = d2+1
Polynomial Roots Calculator is a set of methods aimed at finding values of d for which F(d)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers d 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 2.00
1 1 1.00 2.00
Polynomial Roots Calculator found no rational roots
Equation at the end of step
1
:
(d2 + 1) • (d + 1) = 0
STEP
2
:
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.