What are the solutions to the equation 7x^3-47x^2+121x-65=0 ?

The solutions to the equation 7x^3-47x^2+121x-65=0 are x= 5/7 ,x=3+2i,x=3-2i

Find the zeros of 7x^3-47x^2+121x-65=0

The zeros of 7x^3-47x^2+121x-65=0 are x= 5/7 ,x=3+2i,x=3-2i

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7 x^{3} - 47 x^{2} + 121 x - 65 = 0

x = \frac{5}{7}, x = 3 + 2 i, x = 3 - 2 i

Solution steps

7 x^{3} - 47 x^{2} + 121 x - 65 = 0

Factor

7 x^{3} - 47 x^{2} + 121 x - 65 : (7 x - 5) (x^{2} - 6 x + 13)

(7 x - 5) (x^{2} - 6 x + 13) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

7 x - 5 = 0 or x^{2} - 6 x + 13 = 0

Solve

7 x - 5 = 0 : x = \frac{5}{7}

Solve

x^{2} - 6 x + 13 = 0 : x = 3 + 2 i, x = 3 - 2 i

The solutions are

x = \frac{5}{7}, x = 3 + 2 i, x = 3 - 2 i

x^{2} - 4 = x^{3} - 2 x^{2}

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

x^{4} + x^{2} = \frac{4}{5}

5 x^{4} - 80 = 0

2 x^{3} + x^{2} - 26 x - 13 = 0

What are the solutions to the equation 7x^3-47x^2+121x-65=0 ?
The solutions to the equation 7x^3-47x^2+121x-65=0 are x= 5/7 ,x=3+2i,x=3-2i
Find the zeros of 7x^3-47x^2+121x-65=0
The zeros of 7x^3-47x^2+121x-65=0 are x= 5/7 ,x=3+2i,x=3-2i