What are the solutions to the equation x^4-4x^3-24x^2+20x+7=0 ?

The solutions to the equation x^4-4x^3-24x^2+20x+7=0 are x=1,x=7,x=-2+sqrt(3),x=-2-sqrt(3)

Find the zeros of x^4-4x^3-24x^2+20x+7=0

The zeros of x^4-4x^3-24x^2+20x+7=0 are x=1,x=7,x=-2+sqrt(3),x=-2-sqrt(3)

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x^{4} - 4 x^{3} - 24 x^{2} + 20 x + 7 = 0

x = 1, x = 7, x = - 2 + 3, x = - 2 - 3

Decimal Notation

x = 1, x = 7, x = - 0.26794 \dots, x = - 3.73205 \dots

Solution steps

x^{4} - 4 x^{3} - 24 x^{2} + 20 x + 7 = 0

Factor

x^{4} - 4 x^{3} - 24 x^{2} + 20 x + 7 : (x - 1) (x - 7) (x^{2} + 4 x + 1)

(x - 1) (x - 7) (x^{2} + 4 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x - 7 = 0 or x^{2} + 4 x + 1 = 0

Solve

x - 1 = 0 : x = 1

Solve

x - 7 = 0 : x = 7

Solve

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

The solutions are

x = 1, x = 7, x = - 2 + 3, x = - 2 - 3

x = 9 x^{6} x 1 0^{22} x 1 0^{23}

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

4 x (x + 1) (x - 1) = 0

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

(z + 1)^{4} + 16 = 0

What are the solutions to the equation x^4-4x^3-24x^2+20x+7=0 ?
The solutions to the equation x^4-4x^3-24x^2+20x+7=0 are x=1,x=7,x=-2+sqrt(3),x=-2-sqrt(3)
Find the zeros of x^4-4x^3-24x^2+20x+7=0
The zeros of x^4-4x^3-24x^2+20x+7=0 are x=1,x=7,x=-2+sqrt(3),x=-2-sqrt(3)