What are the solutions to the equation x^4-5x^3+x^2-2x-15=0 ?

The solutions to the equation x^4-5x^3+x^2-2x-15=0 are x=5,x\approx-1.21341…

Find the zeros of x^4-5x^3+x^2-2x-15=0

The zeros of x^4-5x^3+x^2-2x-15=0 are x=5,x\approx-1.21341…

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x^{4} - 5 x^{3} + x^{2} - 2 x - 15 = 0

x = 5, x \approx - 1.21341 \dots

Solution steps

x^{4} - 5 x^{3} + x^{2} - 2 x - 15 = 0

Factor

x^{4} - 5 x^{3} + x^{2} - 2 x - 15 : (x - 5) (x^{3} + x + 3)

(x - 5) (x^{3} + x + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 5 = 0 or x^{3} + x + 3 = 0

Solve

x - 5 = 0 : x = 5

Solve

x^{3} + x + 3 = 0 : x \approx - 1.21341 \dots

The solutions are

x = 5, x \approx - 1.21341 \dots

x^{3} = 9 x^{2} - 20 x

(3 x - 8) (x + 2) = 2 x^{3}

x^{3} - 6 x - 9 = 0

3 x^{5} - 20 x^{3} + 16 = 0

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

What are the solutions to the equation x^4-5x^3+x^2-2x-15=0 ?
The solutions to the equation x^4-5x^3+x^2-2x-15=0 are x=5,x\approx-1.21341…
Find the zeros of x^4-5x^3+x^2-2x-15=0
The zeros of x^4-5x^3+x^2-2x-15=0 are x=5,x\approx-1.21341…