What are the solutions to the equation r^5-r^4-4r^3-4r^2-5r-3=0 ?

The solutions to the equation r^5-r^4-4r^3-4r^2-5r-3=0 are r=-1,r=3,r=i,r=-i

Find the zeros of r^5-r^4-4r^3-4r^2-5r-3=0

The zeros of r^5-r^4-4r^3-4r^2-5r-3=0 are r=-1,r=3,r=i,r=-i

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r^{5} - r^{4} - 4 r^{3} - 4 r^{2} - 5 r - 3 = 0

r = - 1, r = 3, r = i, r = - i

Solution steps

r^{5} - r^{4} - 4 r^{3} - 4 r^{2} - 5 r - 3 = 0

Factor

r^{5} - r^{4} - 4 r^{3} - 4 r^{2} - 5 r - 3 : (r + 1)^{2} (r - 3) (r^{2} + 1)

(r + 1)^{2} (r - 3) (r^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

r + 1 = 0 or r - 3 = 0 or r^{2} + 1 = 0

Solve

r + 1 = 0 : r = - 1

Solve

r - 3 = 0 : r = 3

Solve

r^{2} + 1 = 0 : r = i, r = - i

The solutions are

r = - 1, r = 3, r = i, r = - i

x^{4} - 12 x^{3} - 14 x^{2} + 292 x + 577 = 0

2 x^{4} + 3 = 0

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

s^{3} + 6 s^{2} + 8 s + 10 = 0

z^{4} + 2 z^{2} + 4 = 0

What are the solutions to the equation r^5-r^4-4r^3-4r^2-5r-3=0 ?
The solutions to the equation r^5-r^4-4r^3-4r^2-5r-3=0 are r=-1,r=3,r=i,r=-i
Find the zeros of r^5-r^4-4r^3-4r^2-5r-3=0
The zeros of r^5-r^4-4r^3-4r^2-5r-3=0 are r=-1,r=3,r=i,r=-i