What are the solutions to the equation x^3-9x^2+3x+45=0 ?

The solutions to the equation x^3-9x^2+3x+45=0 are x=3,x=3+2sqrt(6),x=3-2sqrt(6)

Find the zeros of x^3-9x^2+3x+45=0

The zeros of x^3-9x^2+3x+45=0 are x=3,x=3+2sqrt(6),x=3-2sqrt(6)

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x^{3} - 9 x^{2} + 3 x + 45 = 0

x = 3, x = 3 + 26, x = 3 - 26

Decimal Notation

x = 3, x = 7.89897 \dots, x = - 1.89897 \dots

Solution steps

x^{3} - 9 x^{2} + 3 x + 45 = 0

Factor

x^{3} - 9 x^{2} + 3 x + 45 : (x - 3) (x^{2} - 6 x - 15)

(x - 3) (x^{2} - 6 x - 15) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x^{2} - 6 x - 15 = 0

Solve

x - 3 = 0 : x = 3

Solve

x^{2} - 6 x - 15 = 0 : x = 3 + 26, x = 3 - 26

The solutions are

x = 3, x = 3 + 26, x = 3 - 26

(x^{2} - 1) (x^{2} - 11) (x^{2} - 21) (x^{2} - 31) = - 4224

(3 x + 1)^{3} = 100

(4 x - 1)^{5} = 1

(x - 6)^{4} + (x - 8)^{4} = 16

x^{3} - 6 x^{2} + 3 x + 9 = 0

What are the solutions to the equation x^3-9x^2+3x+45=0 ?
The solutions to the equation x^3-9x^2+3x+45=0 are x=3,x=3+2sqrt(6),x=3-2sqrt(6)
Find the zeros of x^3-9x^2+3x+45=0
The zeros of x^3-9x^2+3x+45=0 are x=3,x=3+2sqrt(6),x=3-2sqrt(6)