What are the solutions to the equation 4x^3-24x^2-9x+54=0 ?

The solutions to the equation 4x^3-24x^2-9x+54=0 are x=6,x=-3/2 ,x= 3/2

Find the zeros of 4x^3-24x^2-9x+54=0

The zeros of 4x^3-24x^2-9x+54=0 are x=6,x=-3/2 ,x= 3/2

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4 x^{3} - 24 x^{2} - 9 x + 54 = 0

x = 6, x = - \frac{3}{2}, x = \frac{3}{2}

Decimal Notation

x = 6, x = - 1.5, x = 1.5

Solution steps

4 x^{3} - 24 x^{2} - 9 x + 54 = 0

Factor

4 x^{3} - 24 x^{2} - 9 x + 54 : (x - 6) (2 x + 3) (2 x - 3)

(x - 6) (2 x + 3) (2 x - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 6 = 0 or 2 x + 3 = 0 or 2 x - 3 = 0

Solve

x - 6 = 0 : x = 6

Solve

2 x + 3 = 0 : x = - \frac{3}{2}

Solve

2 x - 3 = 0 : x = \frac{3}{2}

The solutions are

x = 6, x = - \frac{3}{2}, x = \frac{3}{2}

x^{5} = 3

x^{5} = 7

x^{5} = 8

5 x^{3} = 40

2 x^{3} + 7 x^{2} - 28 x - 98 = 0

What are the solutions to the equation 4x^3-24x^2-9x+54=0 ?
The solutions to the equation 4x^3-24x^2-9x+54=0 are x=6,x=-3/2 ,x= 3/2
Find the zeros of 4x^3-24x^2-9x+54=0
The zeros of 4x^3-24x^2-9x+54=0 are x=6,x=-3/2 ,x= 3/2