What are the solutions to the equation x^3-7x^2+x-7=x^2+1 ?

The solutions to the equation x^3-7x^2+x-7=x^2+1 are x=8,x=i,x=-i

Find the zeros of x^3-7x^2+x-7=x^2+1

The zeros of x^3-7x^2+x-7=x^2+1 are x=8,x=i,x=-i

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x^{3} - 7 x^{2} + x - 7 = x^{2} + 1

x = 8, x = i, x = - i

Solution steps

x^{3} - 7 x^{2} + x - 7 = x^{2} + 1

Move

1

to the left side

x^{3} - 7 x^{2} + x - 8 = x^{2}

Move

x^{2}

to the left side

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

Factor

x^{3} - 8 x^{2} + x - 8 : (x - 8) (x^{2} + 1)

(x - 8) (x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 8 = 0 or x^{2} + 1 = 0

Solve

x - 8 = 0 : x = 8

Solve

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

The solutions are

x = 8, x = i, x = - i

3 x^{4} - 27 x^{2} = 0

x^{3} - 7 x^{2} + 14 x - 6 = 0

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

u^{3} = 8000

\frac{1}{3} x^{3} - 2 x = 0

What are the solutions to the equation x^3-7x^2+x-7=x^2+1 ?
The solutions to the equation x^3-7x^2+x-7=x^2+1 are x=8,x=i,x=-i
Find the zeros of x^3-7x^2+x-7=x^2+1
The zeros of x^3-7x^2+x-7=x^2+1 are x=8,x=i,x=-i