What are the solutions to the equation x^4+25x^2-30x^2+150x-10x^3=216 ?

The solutions to the equation x^4+25x^2-30x^2+150x-10x^3=216 are x=2,x=3,x=-4,x=9

Find the zeros of x^4+25x^2-30x^2+150x-10x^3=216

The zeros of x^4+25x^2-30x^2+150x-10x^3=216 are x=2,x=3,x=-4,x=9

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x^{4} + 25 x^{2} - 30 x^{2} + 150 x - 10 x^{3} = 216

x = 2, x = 3, x = - 4, x = 9

Solution steps

x^{4} + 25 x^{2} - 30 x^{2} + 150 x - 10 x^{3} = 216

Refine

x^{4} - 5 x^{2} + 150 x - 10 x^{3} = 216

Move

216

to the left side

x^{4} - 5 x^{2} + 150 x - 10 x^{3} - 216 = 0

Write in the standard form

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

x^{4} - 10 x^{3} - 5 x^{2} + 150 x - 216 = 0

Factor

x^{4} - 10 x^{3} - 5 x^{2} + 150 x - 216 : (x - 2) (x - 3) (x + 4) (x - 9)

(x - 2) (x - 3) (x + 4) (x - 9) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x - 3 = 0 or x + 4 = 0 or x - 9 = 0

Solve

x - 2 = 0 : x = 2

Solve

x - 3 = 0 : x = 3

Solve

x + 4 = 0 : x = - 4

Solve

x - 9 = 0 : x = 9

The solutions are

x = 2, x = 3, x = - 4, x = 9

x^{1} + x^{2} + x^{3} = 4

11 x^{4} - 7 x^{2} - 4 = 0

(x + 1)^{3} = 0

5 x^{3} + 2 x^{2} - 2 x + 1 = 0

x^{4} = 5 x^{2} - 6

What are the solutions to the equation x^4+25x^2-30x^2+150x-10x^3=216 ?
The solutions to the equation x^4+25x^2-30x^2+150x-10x^3=216 are x=2,x=3,x=-4,x=9
Find the zeros of x^4+25x^2-30x^2+150x-10x^3=216
The zeros of x^4+25x^2-30x^2+150x-10x^3=216 are x=2,x=3,x=-4,x=9