What are the solutions to the equation x^4+6x^3+x^2-24x+16=0 ?

The solutions to the equation x^4+6x^3+x^2-24x+16=0 are x=1,x=-4

Find the zeros of x^4+6x^3+x^2-24x+16=0

The zeros of x^4+6x^3+x^2-24x+16=0 are x=1,x=-4

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x^{4} + 6 x^{3} + x^{2} - 24 x + 16 = 0

x = 1, x = - 4

Solution steps

x^{4} + 6 x^{3} + x^{2} - 24 x + 16 = 0

Factor

x^{4} + 6 x^{3} + x^{2} - 24 x + 16 : (x - 1)^{2} (x + 4)^{2}

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x + 4 = 0

Solve

x - 1 = 0 : x = 1

Solve

x + 4 = 0 : x = - 4

The solutions are

x = 1, x = - 4

x^{2} - 6 x^{3} = 0

6 x^{3} + 4 x^{2} = 2 x + 7

x^{4} - 5 x^{3} - 5 x^{2} + 23 x + 10 = 0

2300000 = 2000000 \cdot (1 + x)^{6}

13 + x^{3} = 7 x^{2} + 13

What are the solutions to the equation x^4+6x^3+x^2-24x+16=0 ?
The solutions to the equation x^4+6x^3+x^2-24x+16=0 are x=1,x=-4
Find the zeros of x^4+6x^3+x^2-24x+16=0
The zeros of x^4+6x^3+x^2-24x+16=0 are x=1,x=-4