What are the solutions to the equation 2x^4-9x^3+17x^2-36x+36=0 ?

The solutions to the equation 2x^4-9x^3+17x^2-36x+36=0 are x=3,x= 3/2 ,x=2i,x=-2i

Find the zeros of 2x^4-9x^3+17x^2-36x+36=0

The zeros of 2x^4-9x^3+17x^2-36x+36=0 are x=3,x= 3/2 ,x=2i,x=-2i

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2 x^{4} - 9 x^{3} + 17 x^{2} - 36 x + 36 = 0

x = 3, x = \frac{3}{2}, x = 2 i, x = - 2 i

Solution steps

2 x^{4} - 9 x^{3} + 17 x^{2} - 36 x + 36 = 0

Factor

2 x^{4} - 9 x^{3} + 17 x^{2} - 36 x + 36 : (x - 3) (2 x - 3) (x^{2} + 4)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 3 = 0 : x = 3

Solve

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

Solve

x^{2} + 4 = 0 : x = 2 i, x = - 2 i

The solutions are

x = 3, x = \frac{3}{2}, x = 2 i, x = - 2 i

x^{4} + 7 x^{3} + 8 x^{2} - 7 x + 15 = 0

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

x^{3} + 5 x^{2} - 13 x + 7 = 0

x^{3} + 5 x^{2} + 24 x + 20 = 0

3 x^{2} (x - 1) - 2 = x^{2}

What are the solutions to the equation 2x^4-9x^3+17x^2-36x+36=0 ?
The solutions to the equation 2x^4-9x^3+17x^2-36x+36=0 are x=3,x= 3/2 ,x=2i,x=-2i
Find the zeros of 2x^4-9x^3+17x^2-36x+36=0
The zeros of 2x^4-9x^3+17x^2-36x+36=0 are x=3,x= 3/2 ,x=2i,x=-2i