What are the solutions to the equation 2x^4-5x^3-20x^2+115x-52=0 ?

The solutions to the equation 2x^4-5x^3-20x^2+115x-52=0 are x=-4,x= 1/2 ,x=3+2i,x=3-2i

Find the zeros of 2x^4-5x^3-20x^2+115x-52=0

The zeros of 2x^4-5x^3-20x^2+115x-52=0 are x=-4,x= 1/2 ,x=3+2i,x=3-2i

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2 x^{4} - 5 x^{3} - 20 x^{2} + 115 x - 52 = 0

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

Solution steps

2 x^{4} - 5 x^{3} - 20 x^{2} + 115 x - 52 = 0

Factor

2 x^{4} - 5 x^{3} - 20 x^{2} + 115 x - 52 : (x + 4) (2 x - 1) (x^{2} - 6 x + 13)

(x + 4) (2 x - 1) (x^{2} - 6 x + 13) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 4 = 0 or 2 x - 1 = 0 or x^{2} - 6 x + 13 = 0

Solve

x + 4 = 0 : x = - 4

Solve

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

Solve

x^{2} - 6 x + 13 = 0 : x = 3 + 2 i, x = 3 - 2 i

The solutions are

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

4 x^{3} - 36 x^{2} + 104 x - 96 = 0

z^{3} = (- 3 + i)

2 x^{3} + 2 x^{2} - 19 x + 20 = 0

3 x^{3} + 7 x^{2} - 4 = 0

y, x = y^{3} - 1

What are the solutions to the equation 2x^4-5x^3-20x^2+115x-52=0 ?
The solutions to the equation 2x^4-5x^3-20x^2+115x-52=0 are x=-4,x= 1/2 ,x=3+2i,x=3-2i
Find the zeros of 2x^4-5x^3-20x^2+115x-52=0
The zeros of 2x^4-5x^3-20x^2+115x-52=0 are x=-4,x= 1/2 ,x=3+2i,x=3-2i