What are the solutions to the equation r^4+10r^3-9^2-90r=0 ?

The solutions to the equation r^4+10r^3-9^2-90r=0 are r=-1,r=-9,r=-3,r=3

Find the zeros of r^4+10r^3-9^2-90r=0

The zeros of r^4+10r^3-9^2-90r=0 are r=-1,r=-9,r=-3,r=3

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r^{4} + 10 r^{3} - 9^{2} - 90 r = 0

r = - 1, r = - 9, r = - 3, r = 3

Solution steps

r^{4} + 10 r^{3} - 9^{2} - 90 r = 0

Expand

r^{4} + 10 r^{3} - 9^{2} - 90 r : r^{4} + 10 r^{3} - 81 - 90 r

r^{4} + 10 r^{3} - 81 - 90 r = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

r^{4} + 10 r^{3} - 90 r - 81 = 0

Factor

r^{4} + 10 r^{3} - 90 r - 81 : (r + 1) (r + 9) (r + 3) (r - 3)

(r + 1) (r + 9) (r + 3) (r - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

r + 1 = 0 or r + 9 = 0 or r + 3 = 0 or r - 3 = 0

Solve

r + 1 = 0 : r = - 1

Solve

r + 9 = 0 : r = - 9

Solve

r + 3 = 0 : r = - 3

Solve

r - 3 = 0 : r = 3

The solutions are

r = - 1, r = - 9, r = - 3, r = 3

12 x^{3} - 12 x^{2} - 72 x = 0

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

s (2 s + 0.1)^{2} = 8 \cdot 1 0^{- 9}

3 x^{3} - x - 10 x = - x^{2} + 2 x

x^{4} - a^{4} = 0

What are the solutions to the equation r^4+10r^3-9^2-90r=0 ?
The solutions to the equation r^4+10r^3-9^2-90r=0 are r=-1,r=-9,r=-3,r=3
Find the zeros of r^4+10r^3-9^2-90r=0
The zeros of r^4+10r^3-9^2-90r=0 are r=-1,r=-9,r=-3,r=3