What are the solutions to the equation x^4+8x^3+3x-12=0 ?

The solutions to the equation x^4+8x^3+3x-12=0 are x=1,x\approx-8.06891…

Find the zeros of x^4+8x^3+3x-12=0

The zeros of x^4+8x^3+3x-12=0 are x=1,x\approx-8.06891…

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x^{4} + 8 x^{3} + 3 x - 12 = 0

x = 1, x \approx - 8.06891 \dots

Solution steps

x^{4} + 8 x^{3} + 3 x - 12 = 0

Factor

x^{4} + 8 x^{3} + 3 x - 12 : (x - 1) (x^{3} + 9 x^{2} + 9 x + 12)

(x - 1) (x^{3} + 9 x^{2} + 9 x + 12) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{3} + 9 x^{2} + 9 x + 12 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{3} + 9 x^{2} + 9 x + 12 = 0 : x \approx - 8.06891 \dots

The solutions are

x = 1, x \approx - 8.06891 \dots

x^{5} - 2 = 30

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

3 x^{4} + 12 x^{2} = 6 x^{3}

x^{3} + x^{2} = 1

(m + 1)^{3} = 0

What are the solutions to the equation x^4+8x^3+3x-12=0 ?
The solutions to the equation x^4+8x^3+3x-12=0 are x=1,x\approx-8.06891…
Find the zeros of x^4+8x^3+3x-12=0
The zeros of x^4+8x^3+3x-12=0 are x=1,x\approx-8.06891…