What are the solutions to the equation 0=x^2-2x^3-10x+11 ?

The solutions to the equation 0=x^2-2x^3-10x+11 are x=1,x=-1/4+i(sqrt(87))/4 ,x=-1/4-i(sqrt(87))/4

Find the zeros of 0=x^2-2x^3-10x+11

The zeros of 0=x^2-2x^3-10x+11 are x=1,x=-1/4+i(sqrt(87))/4 ,x=-1/4-i(sqrt(87))/4

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0 = x^{2} - 2 x^{3} - 10 x + 11

x = 1, x = - \frac{1}{4} + i \frac{87}{4}, x = - \frac{1}{4} - i \frac{87}{4}

Solution steps

0 = x^{2} - 2 x^{3} - 10 x + 11

Switch sides

x^{2} - 2 x^{3} - 10 x + 11 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 2 x^{3} + x^{2} - 10 x + 11 = 0

Factor

- 2 x^{3} + x^{2} - 10 x + 11 : - (x - 1) (2 x^{2} + x + 11)

- (x - 1) (2 x^{2} + x + 11) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or 2 x^{2} + x + 11 = 0

Solve

x - 1 = 0 : x = 1

Solve

2 x^{2} + x + 11 = 0 : x = - \frac{1}{4} + i \frac{87}{4}, x = - \frac{1}{4} - i \frac{87}{4}

The solutions are

x = 1, x = - \frac{1}{4} + i \frac{87}{4}, x = - \frac{1}{4} - i \frac{87}{4}

3 x^{4} + 5 x^{3} - 11 x^{2} + 2 x - 3 = 0

x^{2} (x^{2} - 81) - 49 (x^{2} - 81) = 0

3 x^{3} - 5 x^{2} - 1 = 0

(x + 2)^{4} = 81

5 = 4 x^{3} + 12 x^{2} + 12 x + 4

What are the solutions to the equation 0=x^2-2x^3-10x+11 ?
The solutions to the equation 0=x^2-2x^3-10x+11 are x=1,x=-1/4+i(sqrt(87))/4 ,x=-1/4-i(sqrt(87))/4
Find the zeros of 0=x^2-2x^3-10x+11
The zeros of 0=x^2-2x^3-10x+11 are x=1,x=-1/4+i(sqrt(87))/4 ,x=-1/4-i(sqrt(87))/4