What are the solutions to the equation x^3-11x^2+37x-42=0 ?

The solutions to the equation x^3-11x^2+37x-42=0 are x=6,x= 5/2+i(sqrt(3))/2 ,x= 5/2-i(sqrt(3))/2

Find the zeros of x^3-11x^2+37x-42=0

The zeros of x^3-11x^2+37x-42=0 are x=6,x= 5/2+i(sqrt(3))/2 ,x= 5/2-i(sqrt(3))/2

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x^{3} - 11 x^{2} + 37 x - 42 = 0

x = 6, x = \frac{5}{2} + i \frac{3}{2}, x = \frac{5}{2} - i \frac{3}{2}

Solution steps

x^{3} - 11 x^{2} + 37 x - 42 = 0

Factor

x^{3} - 11 x^{2} + 37 x - 42 : (x - 6) (x^{2} - 5 x + 7)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 6 = 0 : x = 6

Solve

x^{2} - 5 x + 7 = 0 : x = \frac{5}{2} + i \frac{3}{2}, x = \frac{5}{2} - i \frac{3}{2}

The solutions are

x = 6, x = \frac{5}{2} + i \frac{3}{2}, x = \frac{5}{2} - i \frac{3}{2}

- X^{3} + 9 X^{2} - 24 X + 20 = 0

x^{3} + x^{2} = 6 x

(5 x - 2)^{3} - (5 x - 2) = 0

(x + 1)^{3} + x + 1 = 0

x^{3} + 25.3 x^{2} + 219.5 x + 660.1 = 0

What are the solutions to the equation x^3-11x^2+37x-42=0 ?
The solutions to the equation x^3-11x^2+37x-42=0 are x=6,x= 5/2+i(sqrt(3))/2 ,x= 5/2-i(sqrt(3))/2
Find the zeros of x^3-11x^2+37x-42=0
The zeros of x^3-11x^2+37x-42=0 are x=6,x= 5/2+i(sqrt(3))/2 ,x= 5/2-i(sqrt(3))/2