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

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

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

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

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

r = 2, r = 1 + i, r = 1 - i

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

r - 2 = 0 : r = 2

Solve

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

The solutions are

r = 2, r = 1 + i, r = 1 - i

8 n^{3} - 4 n^{2} = 18 n - 9

x^{3} - 8 x - 3 = 0

15.625 = s^{3}

x^{4} - 5 x^{2} + 2 x + 11 = 0

(x - 1)^{3} - 54 = 0

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