What are the solutions to the equation x^4-5x^3+7x^2-5x+6=0 ?

The solutions to the equation x^4-5x^3+7x^2-5x+6=0 are x=2,x=3,x=i,x=-i

Find the zeros of x^4-5x^3+7x^2-5x+6=0

The zeros of x^4-5x^3+7x^2-5x+6=0 are x=2,x=3,x=i,x=-i

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x^{4} - 5 x^{3} + 7 x^{2} - 5 x + 6 = 0

x = 2, x = 3, x = i, x = - i

Solution steps

x^{4} - 5 x^{3} + 7 x^{2} - 5 x + 6 = 0

Factor

x^{4} - 5 x^{3} + 7 x^{2} - 5 x + 6 : (x - 2) (x - 3) (x^{2} + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

x - 3 = 0 : x = 3

Solve

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

The solutions are

x = 2, x = 3, x = i, x = - i

72 x^{7} - 504 x^{6} = 0

x + 3 = x^{3} + 10 x^{2} + 28 x + 21

x^{3} - 5 x^{2} + 8 x - 4

2 x^{4} + 9 x^{3} + 15 x^{2} + 11 x + 3 = 0

x^{3} + x^{2} - 4 x - 4

What are the solutions to the equation x^4-5x^3+7x^2-5x+6=0 ?
The solutions to the equation x^4-5x^3+7x^2-5x+6=0 are x=2,x=3,x=i,x=-i
Find the zeros of x^4-5x^3+7x^2-5x+6=0
The zeros of x^4-5x^3+7x^2-5x+6=0 are x=2,x=3,x=i,x=-i