What are the solutions to the equation x^4-4x^3-x^2+14x+10=0 ?

The solutions to the equation x^4-4x^3-x^2+14x+10=0 are x=-1,x=3+i,x=3-i

Find the zeros of x^4-4x^3-x^2+14x+10=0

The zeros of x^4-4x^3-x^2+14x+10=0 are x=-1,x=3+i,x=3-i

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x^{4} - 4 x^{3} - x^{2} + 14 x + 10 = 0

x = - 1, x = 3 + i, x = 3 - i

Solution steps

x^{4} - 4 x^{3} - x^{2} + 14 x + 10 = 0

Factor

x^{4} - 4 x^{3} - x^{2} + 14 x + 10 : (x + 1)^{2} (x^{2} - 6 x + 10)

(x + 1)^{2} (x^{2} - 6 x + 10) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x^{2} - 6 x + 10 = 0

Solve

x + 1 = 0 : x = - 1

Solve

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

The solutions are

x = - 1, x = 3 + i, x = 3 - i

x^{3} - 5 x - 6 = 0

x^{3} + 8 x^{2} + 12 x + 18 = 0

- 4 x^{3} - 18 x^{2} - 32 x - 26 = 0

x^{4} + 5 x = 0

x^{3} + 12 x^{2} + 32 x = 0

What are the solutions to the equation x^4-4x^3-x^2+14x+10=0 ?
The solutions to the equation x^4-4x^3-x^2+14x+10=0 are x=-1,x=3+i,x=3-i
Find the zeros of x^4-4x^3-x^2+14x+10=0
The zeros of x^4-4x^3-x^2+14x+10=0 are x=-1,x=3+i,x=3-i