What are the solutions to the equation x^4+6x^3-5x^2-24x+4=0 ?

The solutions to the equation x^4+6x^3-5x^2-24x+4=0 are x=-2,x=2,x=-3+sqrt(10),x=-3-sqrt(10)

Find the zeros of x^4+6x^3-5x^2-24x+4=0

The zeros of x^4+6x^3-5x^2-24x+4=0 are x=-2,x=2,x=-3+sqrt(10),x=-3-sqrt(10)

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x^{4} + 6 x^{3} - 5 x^{2} - 24 x + 4 = 0

x = - 2, x = 2, x = - 3 + 10, x = - 3 - 10

Decimal Notation

x = - 2, x = 2, x = 0.16227 \dots, x = - 6.16227 \dots

Solution steps

x^{4} + 6 x^{3} - 5 x^{2} - 24 x + 4 = 0

Factor

x^{4} + 6 x^{3} - 5 x^{2} - 24 x + 4 : (x + 2) (x - 2) (x^{2} + 6 x - 1)

(x + 2) (x - 2) (x^{2} + 6 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 2 = 0 : x = - 2

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + 6 x - 1 = 0 : x = - 3 + 10, x = - 3 - 10

The solutions are

x = - 2, x = 2, x = - 3 + 10, x = - 3 - 10

x^{4} + 6 x^{3} + 8 x^{2} - 6 x - 9 = 0

x^{4} - 9 x^{3} + 27 x^{2} - 27 x = 0

x^{5} - 3 \cdot x^{2} + x + 1 = 0

x^{3} + 3 x^{2} - 18 x - 40 = 0

y, 25 x^{4} - 625 y - 500 = 0

What are the solutions to the equation x^4+6x^3-5x^2-24x+4=0 ?
The solutions to the equation x^4+6x^3-5x^2-24x+4=0 are x=-2,x=2,x=-3+sqrt(10),x=-3-sqrt(10)
Find the zeros of x^4+6x^3-5x^2-24x+4=0
The zeros of x^4+6x^3-5x^2-24x+4=0 are x=-2,x=2,x=-3+sqrt(10),x=-3-sqrt(10)