What are the solutions to the equation 12x^4+64x^3+59x^2-23x-12=0 ?

The solutions to the equation 12x^4+64x^3+59x^2-23x-12=0 are x=-4,x= 1/2 ,x=-1/3 ,x=-3/2

Find the zeros of 12x^4+64x^3+59x^2-23x-12=0

The zeros of 12x^4+64x^3+59x^2-23x-12=0 are x=-4,x= 1/2 ,x=-1/3 ,x=-3/2

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12 x^{4} + 64 x^{3} + 59 x^{2} - 23 x - 12 = 0

x = - 4, x = \frac{1}{2}, x = - \frac{1}{3}, x = - \frac{3}{2}

Decimal Notation

x = - 4, x = 0.5, x = - 0.33333 \dots, x = - 1.5

Solution steps

12 x^{4} + 64 x^{3} + 59 x^{2} - 23 x - 12 = 0

Factor

12 x^{4} + 64 x^{3} + 59 x^{2} - 23 x - 12 : (x + 4) (2 x - 1) (3 x + 1) (2 x + 3)

(x + 4) (2 x - 1) (3 x + 1) (2 x + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 4 = 0 or 2 x - 1 = 0 or 3 x + 1 = 0 or 2 x + 3 = 0

Solve

x + 4 = 0 : x = - 4

Solve

2 x - 1 = 0 : x = \frac{1}{2}

Solve

3 x + 1 = 0 : x = - \frac{1}{3}

Solve

2 x + 3 = 0 : x = - \frac{3}{2}

The solutions are

x = - 4, x = \frac{1}{2}, x = - \frac{1}{3}, x = - \frac{3}{2}

x^{3} = 40

(2 x^{2} - 5 x + 1)^{2} - 16 x^{2} + 40 x - 1 = 0

- x^{3} + 27 x - 54 = 0

(x + 3)^{4} = 16

x^{4} - 5 x^{2} + 4

What are the solutions to the equation 12x^4+64x^3+59x^2-23x-12=0 ?
The solutions to the equation 12x^4+64x^3+59x^2-23x-12=0 are x=-4,x= 1/2 ,x=-1/3 ,x=-3/2
Find the zeros of 12x^4+64x^3+59x^2-23x-12=0
The zeros of 12x^4+64x^3+59x^2-23x-12=0 are x=-4,x= 1/2 ,x=-1/3 ,x=-3/2