What are the solutions to the equation x^3-12x^2+48x-63=0 ?

The solutions to the equation x^3-12x^2+48x-63=0 are x=3,x= 9/2+i(sqrt(3))/2 ,x= 9/2-i(sqrt(3))/2

Find the zeros of x^3-12x^2+48x-63=0

The zeros of x^3-12x^2+48x-63=0 are x=3,x= 9/2+i(sqrt(3))/2 ,x= 9/2-i(sqrt(3))/2

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x^{3} - 12 x^{2} + 48 x - 63 = 0

x = 3, x = \frac{9}{2} + i \frac{3}{2}, x = \frac{9}{2} - i \frac{3}{2}

Solution steps

x^{3} - 12 x^{2} + 48 x - 63 = 0

Factor

x^{3} - 12 x^{2} + 48 x - 63 : (x - 3) (x^{2} - 9 x + 21)

(x - 3) (x^{2} - 9 x + 21) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x^{2} - 9 x + 21 = 0

Solve

x - 3 = 0 : x = 3

Solve

x^{2} - 9 x + 21 = 0 : x = \frac{9}{2} + i \frac{3}{2}, x = \frac{9}{2} - i \frac{3}{2}

The solutions are

x = 3, x = \frac{9}{2} + i \frac{3}{2}, x = \frac{9}{2} - i \frac{3}{2}

0 = x^{3} - 7 x + 6

s, s (s + 2) (s + 10) = 0

(a + y i)^{3} = 4 - 43 + 0 i

4 x^{3} - 8 x^{2} - x + 2 = 0

9 x^{4} - 47 x^{2} + 10 = 0

What are the solutions to the equation x^3-12x^2+48x-63=0 ?
The solutions to the equation x^3-12x^2+48x-63=0 are x=3,x= 9/2+i(sqrt(3))/2 ,x= 9/2-i(sqrt(3))/2
Find the zeros of x^3-12x^2+48x-63=0
The zeros of x^3-12x^2+48x-63=0 are x=3,x= 9/2+i(sqrt(3))/2 ,x= 9/2-i(sqrt(3))/2