What are the solutions to the equation -x^3+24x^2-56x-96=0 ?

The solutions to the equation -x^3+24x^2-56x-96=0 are x=4,x=2(5+sqrt(31)),x=2(5-sqrt(31))

Find the zeros of -x^3+24x^2-56x-96=0

The zeros of -x^3+24x^2-56x-96=0 are x=4,x=2(5+sqrt(31)),x=2(5-sqrt(31))

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- x^{3} + 24 x^{2} - 56 x - 96 = 0

x = 4, x = 2 (5 + 31), x = 2 (5 - 31)

Decimal Notation

x = 4, x = 21.13552 \dots, x = - 1.13552 \dots

Solution steps

- x^{3} + 24 x^{2} - 56 x - 96 = 0

Factor

- x^{3} + 24 x^{2} - 56 x - 96 : - (x - 4) (x^{2} - 20 x - 24)

- (x - 4) (x^{2} - 20 x - 24) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 4 = 0 or x^{2} - 20 x - 24 = 0

Solve

x - 4 = 0 : x = 4

Solve

x^{2} - 20 x - 24 = 0 : x = 2 (5 + 31), x = 2 (5 - 31)

The solutions are

x = 4, x = 2 (5 + 31), x = 2 (5 - 31)

x^{3} - 18 x^{2} + 101 x - 180 = 0

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

4 x^{3} - 100 x = 0

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

x^{3} - 12 x^{2} + 47 x = 60

What are the solutions to the equation -x^3+24x^2-56x-96=0 ?
The solutions to the equation -x^3+24x^2-56x-96=0 are x=4,x=2(5+sqrt(31)),x=2(5-sqrt(31))
Find the zeros of -x^3+24x^2-56x-96=0
The zeros of -x^3+24x^2-56x-96=0 are x=4,x=2(5+sqrt(31)),x=2(5-sqrt(31))