What are the solutions to the equation x^4-3x^3-9x^2+23x-12=0 ?

The solutions to the equation x^4-3x^3-9x^2+23x-12=0 are x=1,x=-3,x=4

Find the zeros of x^4-3x^3-9x^2+23x-12=0

The zeros of x^4-3x^3-9x^2+23x-12=0 are x=1,x=-3,x=4

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x^{4} - 3 x^{3} - 9 x^{2} + 23 x - 12 = 0

x = 1, x = - 3, x = 4

Solution steps

x^{4} - 3 x^{3} - 9 x^{2} + 23 x - 12 = 0

Factor

x^{4} - 3 x^{3} - 9 x^{2} + 23 x - 12 : (x - 1)^{2} (x + 3) (x - 4)

(x - 1)^{2} (x + 3) (x - 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x + 3 = 0 or x - 4 = 0

Solve

x - 1 = 0 : x = 1

Solve

x + 3 = 0 : x = - 3

Solve

x - 4 = 0 : x = 4

The solutions are

x = 1, x = - 3, x = 4

x^{3} + 5 x^{2} - 9 x - 45 = 0

x^{3} - 6 x^{2} - 4 x + 24 = 0

x^{4} - 9 x^{2} - 12 x - 4 = 0

x^{6} - 28 x + 27 = 0

x^{4} - 16 x^{2} + 63 = 0

What are the solutions to the equation x^4-3x^3-9x^2+23x-12=0 ?
The solutions to the equation x^4-3x^3-9x^2+23x-12=0 are x=1,x=-3,x=4
Find the zeros of x^4-3x^3-9x^2+23x-12=0
The zeros of x^4-3x^3-9x^2+23x-12=0 are x=1,x=-3,x=4