What are the solutions to the equation X^3-3X^2+20=0 ?

The solutions to the equation X^3-3X^2+20=0 are X=-2,X= 5/2+i(sqrt(15))/2 ,X= 5/2-i(sqrt(15))/2

Find the zeros of X^3-3X^2+20=0

The zeros of X^3-3X^2+20=0 are X=-2,X= 5/2+i(sqrt(15))/2 ,X= 5/2-i(sqrt(15))/2

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X^{3} - 3 X^{2} + 20 = 0

X = - 2, X = \frac{5}{2} + i \frac{15}{2}, X = \frac{5}{2} - i \frac{15}{2}

Solution steps

X^{3} - 3 X^{2} + 20 = 0

Factor

X^{3} - 3 X^{2} + 20 : (X + 2) (X^{2} - 5 X + 10)

(X + 2) (X^{2} - 5 X + 10) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

X + 2 = 0 or X^{2} - 5 X + 10 = 0

Solve

X + 2 = 0 : X = - 2

Solve

X^{2} - 5 X + 10 = 0 : X = \frac{5}{2} + i \frac{15}{2}, X = \frac{5}{2} - i \frac{15}{2}

The solutions are

X = - 2, X = \frac{5}{2} + i \frac{15}{2}, X = \frac{5}{2} - i \frac{15}{2}

s (s + 3) (s^{2} + 2 s + 2) = 0

\frac{256}{625} = 100 r^{6}

n^{3} = 343

4 X^{3} = 2 X^{2}

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

What are the solutions to the equation X^3-3X^2+20=0 ?
The solutions to the equation X^3-3X^2+20=0 are X=-2,X= 5/2+i(sqrt(15))/2 ,X= 5/2-i(sqrt(15))/2
Find the zeros of X^3-3X^2+20=0
The zeros of X^3-3X^2+20=0 are X=-2,X= 5/2+i(sqrt(15))/2 ,X= 5/2-i(sqrt(15))/2