What are the solutions to the equation 11x^3+17x^2-21x+5=0 ?

The solutions to the equation 11x^3+17x^2-21x+5=0 are x= 5/11 ,x=-1+sqrt(2),x=-1-sqrt(2)

Find the zeros of 11x^3+17x^2-21x+5=0

The zeros of 11x^3+17x^2-21x+5=0 are x= 5/11 ,x=-1+sqrt(2),x=-1-sqrt(2)

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11 x^{3} + 17 x^{2} - 21 x + 5 = 0

x = \frac{5}{11}, x = - 1 + 2, x = - 1 - 2

Decimal

x = 0.45454 \dots, x = 0.41421 \dots, x = - 2.41421 \dots

Solution steps

11 x^{3} + 17 x^{2} - 21 x + 5 = 0

Factor

11 x^{3} + 17 x^{2} - 21 x + 5 : (11 x - 5) (x^{2} + 2 x - 1)

(11 x - 5) (x^{2} + 2 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

11 x - 5 = 0 or x^{2} + 2 x - 1 = 0

Solve

11 x - 5 = 0 : x = \frac{5}{11}

Solve

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

The solutions are

x = \frac{5}{11}, x = - 1 + 2, x = - 1 - 2

x^{3} = 2 - x

x^{3} - 4 x^{2} + 16 x - 64 = 0

x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 1 = 0

4 x^{3} + 8 x^{2} - 32 x = 0

3 y = 4 y^{3}

What are the solutions to the equation 11x^3+17x^2-21x+5=0 ?
The solutions to the equation 11x^3+17x^2-21x+5=0 are x= 5/11 ,x=-1+sqrt(2),x=-1-sqrt(2)
Find the zeros of 11x^3+17x^2-21x+5=0
The zeros of 11x^3+17x^2-21x+5=0 are x= 5/11 ,x=-1+sqrt(2),x=-1-sqrt(2)