What are the solutions to the equation 24x^3-2x^2-5x+1=0 ?

The solutions to the equation 24x^3-2x^2-5x+1=0 are x=-1/2 ,x= 1/4 ,x= 1/3

Find the zeros of 24x^3-2x^2-5x+1=0

The zeros of 24x^3-2x^2-5x+1=0 are x=-1/2 ,x= 1/4 ,x= 1/3

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

x = - \frac{1}{2}, x = \frac{1}{4}, x = \frac{1}{3}

Solution steps

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

Factor

24 x^{3} - 2 x^{2} - 5 x + 1 : (2 x + 1) (4 x - 1) (3 x - 1)

(2 x + 1) (4 x - 1) (3 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x + 1 = 0 or 4 x - 1 = 0 or 3 x - 1 = 0

Solve

2 x + 1 = 0 : x = - \frac{1}{2}

Solve

4 x - 1 = 0 : x = \frac{1}{4}

Solve

3 x - 1 = 0 : x = \frac{1}{3}

The solutions are

x = - \frac{1}{2}, x = \frac{1}{4}, x = \frac{1}{3}

16 x^{4} = 81

x^{4} + x^{3} + 7 x^{2} + 9 x - 18 = 0

x^{9} - 1 = 0

2 a^{3} - 3 a^{2} + 1 = 0

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

What are the solutions to the equation 24x^3-2x^2-5x+1=0 ?
The solutions to the equation 24x^3-2x^2-5x+1=0 are x=-1/2 ,x= 1/4 ,x= 1/3
Find the zeros of 24x^3-2x^2-5x+1=0
The zeros of 24x^3-2x^2-5x+1=0 are x=-1/2 ,x= 1/4 ,x= 1/3