What are the solutions to the equation x^4-x^3-11x^2=x+12 ?

The solutions to the equation x^4-x^3-11x^2=x+12 are x=-3,x=4,x=i,x=-i

Find the zeros of x^4-x^3-11x^2=x+12

The zeros of x^4-x^3-11x^2=x+12 are x=-3,x=4,x=i,x=-i

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x^{4} - x^{3} - 11 x^{2} = x + 12

x = - 3, x = 4, x = i, x = - i

Solution steps

x^{4} - x^{3} - 11 x^{2} = x + 12

Move

12

to the left side

x^{4} - x^{3} - 11 x^{2} - 12 = x

Move

x

to the left side

x^{4} - x^{3} - 11 x^{2} - 12 - x = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{4} - x^{3} - 11 x^{2} - x - 12 = 0

Factor

x^{4} - x^{3} - 11 x^{2} - x - 12 : (x + 3) (x - 4) (x^{2} + 1)

(x + 3) (x - 4) (x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 3 = 0 or x - 4 = 0 or x^{2} + 1 = 0

Solve

x + 3 = 0 : x = - 3

Solve

x - 4 = 0 : x = 4

Solve

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

The solutions are

x = - 3, x = 4, x = i, x = - i

- 3 (9 x^{2} - 4) (x^{2} - 15) = 0

u^{5} = 243

x^{3} + 5 x^{2} - 11 x - 55 = 0

x^{3} + 21 x^{2} + 2520 x + 2500 = 0

(2 x - 3)^{5} = 243

What are the solutions to the equation x^4-x^3-11x^2=x+12 ?
The solutions to the equation x^4-x^3-11x^2=x+12 are x=-3,x=4,x=i,x=-i
Find the zeros of x^4-x^3-11x^2=x+12
The zeros of x^4-x^3-11x^2=x+12 are x=-3,x=4,x=i,x=-i