What are the solutions to the equation 2x^4-3x^3-7x^2-8x+6=0 ?

The solutions to the equation 2x^4-3x^3-7x^2-8x+6=0 are x=3,x= 1/2 ,x=-1+i,x=-1-i

Find the zeros of 2x^4-3x^3-7x^2-8x+6=0

The zeros of 2x^4-3x^3-7x^2-8x+6=0 are x=3,x= 1/2 ,x=-1+i,x=-1-i

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2 x^{4} - 3 x^{3} - 7 x^{2} - 8 x + 6 = 0

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

Solution steps

2 x^{4} - 3 x^{3} - 7 x^{2} - 8 x + 6 = 0

Factor

2 x^{4} - 3 x^{3} - 7 x^{2} - 8 x + 6 : (x - 3) (2 x - 1) (x^{2} + 2 x + 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or 2 x - 1 = 0 or x^{2} + 2 x + 2 = 0

Solve

x - 3 = 0 : x = 3

Solve

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

Solve

x^{2} + 2 x + 2 = 0 : x = - 1 + i, x = - 1 - i

The solutions are

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

- 3 x^{3} + 4 x^{2} - 12 x + 16 = 0

a^{3} + 3 a^{2} + 2 a = 0

y^{4} - 3 y^{2} - 4 = 0

x^{4} - 6 x^{3} + 7 x^{2} + 6 x - 3 = 0

2 y^{2} - 2 y = 12 y^{2} - 12 y^{3}

What are the solutions to the equation 2x^4-3x^3-7x^2-8x+6=0 ?
The solutions to the equation 2x^4-3x^3-7x^2-8x+6=0 are x=3,x= 1/2 ,x=-1+i,x=-1-i
Find the zeros of 2x^4-3x^3-7x^2-8x+6=0
The zeros of 2x^4-3x^3-7x^2-8x+6=0 are x=3,x= 1/2 ,x=-1+i,x=-1-i