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

The solutions to the equation x^3-4x^2+7x-6=0 are x=2,x=1+sqrt(2)i,x=1-sqrt(2)i

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

The zeros of x^3-4x^2+7x-6=0 are x=2,x=1+sqrt(2)i,x=1-sqrt(2)i

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

x = 2, x = 1 + 2 i, x = 1 - 2 i

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

x^{2} - 2 x + 3 = 0 : x = 1 + 2 i, x = 1 - 2 i

The solutions are

x = 2, x = 1 + 2 i, x = 1 - 2 i

(x + 6)^{3} = 0

2 x^{3} + 4 x + 3 = 0

t^{4} - 625 = 0

x^{3} - 10 x - 12 = 0

6 x^{3} = - 54 x

What are the solutions to the equation x^3-4x^2+7x-6=0 ?
The solutions to the equation x^3-4x^2+7x-6=0 are x=2,x=1+sqrt(2)i,x=1-sqrt(2)i
Find the zeros of x^3-4x^2+7x-6=0
The zeros of x^3-4x^2+7x-6=0 are x=2,x=1+sqrt(2)i,x=1-sqrt(2)i