What are the solutions to the equation x^3-14x^2+47x-18=0 ?

The solutions to the equation x^3-14x^2+47x-18=0 are x=9,x=(5+sqrt(17))/2 ,x=(5-sqrt(17))/2

Find the zeros of x^3-14x^2+47x-18=0

The zeros of x^3-14x^2+47x-18=0 are x=9,x=(5+sqrt(17))/2 ,x=(5-sqrt(17))/2

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x^{3} - 14 x^{2} + 47 x - 18 = 0

x = 9, x = \frac{5 + 17}{2}, x = \frac{5 - 17}{2}

Decimal Notation

x = 9, x = 4.56155 \dots, x = 0.43844 \dots

Solution steps

x^{3} - 14 x^{2} + 47 x - 18 = 0

Factor

x^{3} - 14 x^{2} + 47 x - 18 : (x - 9) (x^{2} - 5 x + 2)

(x - 9) (x^{2} - 5 x + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 9 = 0 or x^{2} - 5 x + 2 = 0

Solve

x - 9 = 0 : x = 9

Solve

x^{2} - 5 x + 2 = 0 : x = \frac{5 + 17}{2}, x = \frac{5 - 17}{2}

The solutions are

x = 9, x = \frac{5 + 17}{2}, x = \frac{5 - 17}{2}

- 3 x^{3} = 75 x

16 x^{4} = 625

2 (64 x^{2} - 25) (x^{2} + 49) = 0

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

f^{4} - 4 f^{3} = 25 f

What are the solutions to the equation x^3-14x^2+47x-18=0 ?
The solutions to the equation x^3-14x^2+47x-18=0 are x=9,x=(5+sqrt(17))/2 ,x=(5-sqrt(17))/2
Find the zeros of x^3-14x^2+47x-18=0
The zeros of x^3-14x^2+47x-18=0 are x=9,x=(5+sqrt(17))/2 ,x=(5-sqrt(17))/2