What are the solutions to the equation x^4-3x^3-64=0 ?

The solutions to the equation x^4-3x^3-64=0 are x=4,x\approx-2.29494…

Find the zeros of x^4-3x^3-64=0

The zeros of x^4-3x^3-64=0 are x=4,x\approx-2.29494…

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x^{4} - 3 x^{3} - 64 = 0

x = 4, x \approx - 2.29494 \dots

Solution steps

x^{4} - 3 x^{3} - 64 = 0

Factor

x^{4} - 3 x^{3} - 64 : (x - 4) (x^{3} + x^{2} + 4 x + 16)

(x - 4) (x^{3} + x^{2} + 4 x + 16) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 4 = 0 or x^{3} + x^{2} + 4 x + 16 = 0

Solve

x - 4 = 0 : x = 4

Solve

x^{3} + x^{2} + 4 x + 16 = 0 : x \approx - 2.29494 \dots

The solutions are

x = 4, x \approx - 2.29494 \dots

3 x^{4} + 5 x^{3} - 12 x^{2} - 20 x = 0

x^{2} (2 x - 3)^{3} = 0

6 b^{3} - 9 b^{2} + 2 = 0

x^{3} + 8 x^{2} + 5 x - 14 = 0

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

What are the solutions to the equation x^4-3x^3-64=0 ?
The solutions to the equation x^4-3x^3-64=0 are x=4,x\approx-2.29494…
Find the zeros of x^4-3x^3-64=0
The zeros of x^4-3x^3-64=0 are x=4,x\approx-2.29494…