What are the solutions to the equation r^5+5r^4-2r^3-10r^2+r+5=0 ?

The solutions to the equation r^5+5r^4-2r^3-10r^2+r+5=0 are r=-1,r=1,r=-5

Find the zeros of r^5+5r^4-2r^3-10r^2+r+5=0

The zeros of r^5+5r^4-2r^3-10r^2+r+5=0 are r=-1,r=1,r=-5

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r^{5} + 5 r^{4} - 2 r^{3} - 10 r^{2} + r + 5 = 0

r = - 1, r = 1, r = - 5

Solution steps

r^{5} + 5 r^{4} - 2 r^{3} - 10 r^{2} + r + 5 = 0

Factor

r^{5} + 5 r^{4} - 2 r^{3} - 10 r^{2} + r + 5 : (r + 1)^{2} (r - 1)^{2} (r + 5)

(r + 1)^{2} (r - 1)^{2} (r + 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

r + 1 = 0 or r - 1 = 0 or r + 5 = 0

Solve

r + 1 = 0 : r = - 1

Solve

r - 1 = 0 : r = 1

Solve

r + 5 = 0 : r = - 5

The solutions are

r = - 1, r = 1, r = - 5

x^{3} - 3 x^{2} + 7 x - 5

\frac{1}{3} x^{3} + x^{2} + 1 = 0

(x - 1)^{2} (x - 2) = 0

20 x^{3} + 44 x^{2} - 17 x - 5 = 0

4 x^{5} - 12 x^{4} + 8 x^{3} = 0

What are the solutions to the equation r^5+5r^4-2r^3-10r^2+r+5=0 ?
The solutions to the equation r^5+5r^4-2r^3-10r^2+r+5=0 are r=-1,r=1,r=-5
Find the zeros of r^5+5r^4-2r^3-10r^2+r+5=0
The zeros of r^5+5r^4-2r^3-10r^2+r+5=0 are r=-1,r=1,r=-5