What are the solutions to the equation x^3+6x^2-13x-78=0 ?

The solutions to the equation x^3+6x^2-13x-78=0 are x=-6,x=-sqrt(13),x=sqrt(13)

Find the zeros of x^3+6x^2-13x-78=0

The zeros of x^3+6x^2-13x-78=0 are x=-6,x=-sqrt(13),x=sqrt(13)

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x^{3} + 6 x^{2} - 13 x - 78 = 0

x = - 6, x = - 13, x = 13

Decimal Notation

x = - 6, x = - 3.60555 \dots, x = 3.60555 \dots

Solution steps

x^{3} + 6 x^{2} - 13 x - 78 = 0

Factor

x^{3} + 6 x^{2} - 13 x - 78 : (x + 6) (x + 13) (x - 13)

(x + 6) (x + 13) (x - 13) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 6 = 0 or x + 13 = 0 or x - 13 = 0

Solve

x + 6 = 0 : x = - 6

Solve

x + 13 = 0 : x = - 13

Solve

x - 13 = 0 : x = 13

The solutions are

x = - 6, x = - 13, x = 13

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

x^{4} + 10 x^{2} - 9 = 0

16 x = x^{4}

x^{9} = 72

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

What are the solutions to the equation x^3+6x^2-13x-78=0 ?
The solutions to the equation x^3+6x^2-13x-78=0 are x=-6,x=-sqrt(13),x=sqrt(13)
Find the zeros of x^3+6x^2-13x-78=0
The zeros of x^3+6x^2-13x-78=0 are x=-6,x=-sqrt(13),x=sqrt(13)