What are the solutions to the equation 3x^3+6x-21x^2-42=0 ?

The solutions to the equation 3x^3+6x-21x^2-42=0 are x=7,x=sqrt(2)i,x=-sqrt(2)i

Find the zeros of 3x^3+6x-21x^2-42=0

The zeros of 3x^3+6x-21x^2-42=0 are x=7,x=sqrt(2)i,x=-sqrt(2)i

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3 x^{3} + 6 x - 21 x^{2} - 42 = 0

x = 7, x = 2 i, x = - 2 i

Solution steps

3 x^{3} + 6 x - 21 x^{2} - 42 = 0

Write in the standard form

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

3 x^{3} - 21 x^{2} + 6 x - 42 = 0

Factor

3 x^{3} - 21 x^{2} + 6 x - 42 : 3 (x - 7) (x^{2} + 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 7 = 0 : x = 7

Solve

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

The solutions are

x = 7, x = 2 i, x = - 2 i

\frac{x ^{8} + 1}{( 2 c ^{4} )} = 98

7 a^{3} + 41 - a^{3} = - 52

1 - 3 \cdot (x + 4)^{3} = 25

(z + 1)^{4} = - 1

x^{5} = 2 + x

What are the solutions to the equation 3x^3+6x-21x^2-42=0 ?
The solutions to the equation 3x^3+6x-21x^2-42=0 are x=7,x=sqrt(2)i,x=-sqrt(2)i
Find the zeros of 3x^3+6x-21x^2-42=0
The zeros of 3x^3+6x-21x^2-42=0 are x=7,x=sqrt(2)i,x=-sqrt(2)i