What are the solutions to the equation r^4+4r^3+6r^2+4r+1=0 ?

The solutions to the equation r^4+4r^3+6r^2+4r+1=0 are r=-1

Find the zeros of r^4+4r^3+6r^2+4r+1=0

The zeros of r^4+4r^3+6r^2+4r+1=0 are r=-1

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r^{4} + 4 r^{3} + 6 r^{2} + 4 r + 1 = 0

r = - 1

Solution steps

r^{4} + 4 r^{3} + 6 r^{2} + 4 r + 1 = 0

Factor

r^{4} + 4 r^{3} + 6 r^{2} + 4 r + 1 : (r + 1)^{4}

(r + 1)^{4} = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

r + 1 = 0

Solve

r + 1 = 0 : r = - 1

The solution is

r = - 1

x^{4} - 5 x^{3} + 6 x^{2} = 0

y^{3} + y^{2} = 9 y + 9

54 = x^{4}

(1 - 3 x)^{4} - 5 (1 - 3 x)^{2} + 4 = 0

0 = 4 x^{3} + 16 x - 20

What are the solutions to the equation r^4+4r^3+6r^2+4r+1=0 ?
The solutions to the equation r^4+4r^3+6r^2+4r+1=0 are r=-1
Find the zeros of r^4+4r^3+6r^2+4r+1=0
The zeros of r^4+4r^3+6r^2+4r+1=0 are r=-1