What are the solutions to the equation roots 16x^3-4x^2-20x+5 ?

The solutions to the equation roots 16x^3-4x^2-20x+5 are x= 1/4 ,x=-(sqrt(5))/2 ,x=(sqrt(5))/2

Find the zeros of roots 16x^3-4x^2-20x+5

The zeros of roots 16x^3-4x^2-20x+5 are x= 1/4 ,x=-(sqrt(5))/2 ,x=(sqrt(5))/2

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roots

16 x^{3} - 4 x^{2} - 20 x + 5

x = \frac{1}{4}, x = - \frac{5}{2}, x = \frac{5}{2}

Solution steps

16 x^{3} - 4 x^{2} - 20 x + 5

The roots are the intercepts with the x-axis

(y = 0)

16 x^{3} - 4 x^{2} - 20 x + 5 = 0

Factor

16 x^{3} - 4 x^{2} - 20 x + 5 : (4 x - 1) (2 x + 5) (2 x - 5)

(4 x - 1) (2 x + 5) (2 x - 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

4 x - 1 = 0 or 2 x + 5 = 0 or 2 x - 5 = 0

Solve

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

Solve

2 x + 5 = 0 : x = - \frac{5}{2}

Solve

2 x - 5 = 0 : x = \frac{5}{2}

The solutions are

x = \frac{1}{4}, x = - \frac{5}{2}, x = \frac{5}{2}

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

3 (4 x - 3)^{4} = 1875

r^{4} - 2 r^{3} + r^{2} = 0

r^{3} - 5 r^{2} + 3 r + 9 = 0

x^{5} - 10 x^{3} - 20 x^{2} - 15 x - 4 = 0

What are the solutions to the equation roots 16x^3-4x^2-20x+5 ?
The solutions to the equation roots 16x^3-4x^2-20x+5 are x= 1/4 ,x=-(sqrt(5))/2 ,x=(sqrt(5))/2
Find the zeros of roots 16x^3-4x^2-20x+5
The zeros of roots 16x^3-4x^2-20x+5 are x= 1/4 ,x=-(sqrt(5))/2 ,x=(sqrt(5))/2