What are the solutions to the equation 2x^4-15x^3+32x^2-30x+56=0 ?

The solutions to the equation 2x^4-15x^3+32x^2-30x+56=0 are x=4,x= 7/2 ,x=sqrt(2)i,x=-sqrt(2)i

Find the zeros of 2x^4-15x^3+32x^2-30x+56=0

The zeros of 2x^4-15x^3+32x^2-30x+56=0 are x=4,x= 7/2 ,x=sqrt(2)i,x=-sqrt(2)i

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2 x^{4} - 15 x^{3} + 32 x^{2} - 30 x + 56 = 0

x = 4, x = \frac{7}{2}, x = 2 i, x = - 2 i

Solution steps

2 x^{4} - 15 x^{3} + 32 x^{2} - 30 x + 56 = 0

Factor

2 x^{4} - 15 x^{3} + 32 x^{2} - 30 x + 56 : (x - 4) (2 x - 7) (x^{2} + 2)

(x - 4) (2 x - 7) (x^{2} + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 4 = 0 : x = 4

Solve

2 x - 7 = 0 : x = \frac{7}{2}

Solve

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

The solutions are

x = 4, x = \frac{7}{2}, x = 2 i, x = - 2 i

x^{3} - 4 x^{2} - 11 x - 6 = 0

x^{3} - 3 x + 5

y, 4 y - 4 x^{3} = 0

2 x^{3} - 18 x^{2} - 44 x = 0

What are the solutions to the equation 2x^4-15x^3+32x^2-30x+56=0 ?
The solutions to the equation 2x^4-15x^3+32x^2-30x+56=0 are x=4,x= 7/2 ,x=sqrt(2)i,x=-sqrt(2)i
Find the zeros of 2x^4-15x^3+32x^2-30x+56=0
The zeros of 2x^4-15x^3+32x^2-30x+56=0 are x=4,x= 7/2 ,x=sqrt(2)i,x=-sqrt(2)i