What are the solutions to the equation x^4-12x^3+46x^2-60x+16=0 ?

The solutions to the equation x^4-12x^3+46x^2-60x+16=0 are x=2,x=4,x=3+sqrt(7),x=3-sqrt(7)

Find the zeros of x^4-12x^3+46x^2-60x+16=0

The zeros of x^4-12x^3+46x^2-60x+16=0 are x=2,x=4,x=3+sqrt(7),x=3-sqrt(7)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^{4} - 12 x^{3} + 46 x^{2} - 60 x + 16 = 0

x = 2, x = 4, x = 3 + 7, x = 3 - 7

Decimal Notation

x = 2, x = 4, x = 5.64575 \dots, x = 0.35424 \dots

Solution steps

x^{4} - 12 x^{3} + 46 x^{2} - 60 x + 16 = 0

Factor

x^{4} - 12 x^{3} + 46 x^{2} - 60 x + 16 : (x - 2) (x - 4) (x^{2} - 6 x + 2)

(x - 2) (x - 4) (x^{2} - 6 x + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x - 4 = 0 or x^{2} - 6 x + 2 = 0

Solve

x - 2 = 0 : x = 2

Solve

x - 4 = 0 : x = 4

Solve

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

The solutions are

x = 2, x = 4, x = 3 + 7, x = 3 - 7

2 x^{2} = x^{3}

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

n (n + 1) = \frac{n ( n + 1 ) ( n + 2 )}{3}

- 64 = m^{3}

x, 0 = x^{3} - 2 x + 5

What are the solutions to the equation x^4-12x^3+46x^2-60x+16=0 ?
The solutions to the equation x^4-12x^3+46x^2-60x+16=0 are x=2,x=4,x=3+sqrt(7),x=3-sqrt(7)
Find the zeros of x^4-12x^3+46x^2-60x+16=0
The zeros of x^4-12x^3+46x^2-60x+16=0 are x=2,x=4,x=3+sqrt(7),x=3-sqrt(7)