What are the solutions to the equation x^3-3x^2+x-3=x^2+1 ?

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

Find the zeros of x^3-3x^2+x-3=x^2+1

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

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

x = 4, x = i, x = - i

Solution steps

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

Move

1

to the left side

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

Move

x^{2}

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 4 = 0 or x^{2} + 1 = 0

Solve

x - 4 = 0 : x = 4

Solve

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

The solutions are

x = 4, x = i, x = - i

2 x^{3} - 30 x^{2} + 100 x = 0

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

y, y^{3} = x^{2}

x^{5} = 25 x^{3}

x^{3} - 7 x^{2} + 16 x - 12 = 0

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