What are the solutions to the equation x^4-3x^3+5x^2-x-10=0 ?

The solutions to the equation x^4-3x^3+5x^2-x-10=0 are x=-1,x=2,x=1+2i,x=1-2i

Find the zeros of x^4-3x^3+5x^2-x-10=0

The zeros of x^4-3x^3+5x^2-x-10=0 are x=-1,x=2,x=1+2i,x=1-2i

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x^{4} - 3 x^{3} + 5 x^{2} - x - 10 = 0

x = - 1, x = 2, x = 1 + 2 i, x = 1 - 2 i

Solution steps

x^{4} - 3 x^{3} + 5 x^{2} - x - 10 = 0

Factor

x^{4} - 3 x^{3} + 5 x^{2} - x - 10 : (x + 1) (x - 2) (x^{2} - 2 x + 5)

(x + 1) (x - 2) (x^{2} - 2 x + 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x - 2 = 0 or x^{2} - 2 x + 5 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 2 = 0 : x = 2

Solve

x^{2} - 2 x + 5 = 0 : x = 1 + 2 i, x = 1 - 2 i

The solutions are

x = - 1, x = 2, x = 1 + 2 i, x = 1 - 2 i

25 x + 8 x^{2} - 4 x^{3} = 50

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

x^{3} - 14 x^{2} + 48 x = 0

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

x^{3} = \frac{64}{343}

What are the solutions to the equation x^4-3x^3+5x^2-x-10=0 ?
The solutions to the equation x^4-3x^3+5x^2-x-10=0 are x=-1,x=2,x=1+2i,x=1-2i
Find the zeros of x^4-3x^3+5x^2-x-10=0
The zeros of x^4-3x^3+5x^2-x-10=0 are x=-1,x=2,x=1+2i,x=1-2i