What are the solutions to the equation x^4-3x^3+4x^2-3x+1=0 ?

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

Find the zeros of x^4-3x^3+4x^2-3x+1=0

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^{4} - 3 x^{3} + 4 x^{2} - 3 x + 1 = 0

x = 1, x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}

Solution steps

x^{4} - 3 x^{3} + 4 x^{2} - 3 x + 1 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

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

The solutions are

x = 1, x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}

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

9 y^{4} + 65 y^{2} - 144 = 0

x^{3} - 4 x^{2} - x - 1 = 0

x^{4} + x^{3} - 6 x^{2} - 4 x + 8 = 0

x^{3} - 6 x^{2} + 1 = 0

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