What are the solutions to the equation 4x^3-13x^2+4x-3=0 ?

The solutions to the equation 4x^3-13x^2+4x-3=0 are x=3,x= 1/8+i(sqrt(15))/8 ,x= 1/8-i(sqrt(15))/8

Find the zeros of 4x^3-13x^2+4x-3=0

The zeros of 4x^3-13x^2+4x-3=0 are x=3,x= 1/8+i(sqrt(15))/8 ,x= 1/8-i(sqrt(15))/8

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4 x^{3} - 13 x^{2} + 4 x - 3 = 0

x = 3, x = \frac{1}{8} + i \frac{15}{8}, x = \frac{1}{8} - i \frac{15}{8}

Solution steps

4 x^{3} - 13 x^{2} + 4 x - 3 = 0

Factor

4 x^{3} - 13 x^{2} + 4 x - 3 : (x - 3) (4 x^{2} - x + 1)

(x - 3) (4 x^{2} - x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or 4 x^{2} - x + 1 = 0

Solve

x - 3 = 0 : x = 3

Solve

4 x^{2} - x + 1 = 0 : x = \frac{1}{8} + i \frac{15}{8}, x = \frac{1}{8} - i \frac{15}{8}

The solutions are

x = 3, x = \frac{1}{8} + i \frac{15}{8}, x = \frac{1}{8} - i \frac{15}{8}

2 x (100 x^{2} - 9) (x^{2} - 3) = 0

0 = 4 x^{3} - 32

2 x (6 - x)^{3} - 3 x^{2} (6 - x)^{2} = 0

2 x^{4} = 1024 x

2 x^{3} - 1 = x^{6} - 1

What are the solutions to the equation 4x^3-13x^2+4x-3=0 ?
The solutions to the equation 4x^3-13x^2+4x-3=0 are x=3,x= 1/8+i(sqrt(15))/8 ,x= 1/8-i(sqrt(15))/8
Find the zeros of 4x^3-13x^2+4x-3=0
The zeros of 4x^3-13x^2+4x-3=0 are x=3,x= 1/8+i(sqrt(15))/8 ,x= 1/8-i(sqrt(15))/8