Sum of Cubic Roots

Algebra Level 2

Consider the following cubic equation:

x 3 + x + 1 = 0 \large{x^3 + x + 1 = 0}

This equation has three distinct solutions x 1 , x 2 , x 3 x_1, x_2, x_3 . What is ∣ x 1 + x 2 + x 3 ∣ |x_1 + x_2 + x_3| ?

Note: The solutions may be complex, and the ∣ ⋅ ∣ |\cdot| denotes the modulus of a complex number


The answer is 0.0.

Steven Chase by Steven Chase , 37, USA

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1 solution

Henry U
Jan 29, 2019

By Vieta's formula , the sum of the roots of a cubic equation is equal to the coefficient of x 2 x^2 , which in this case is 0 0 , so ∣ 0 ∣ = 0 |0| = \boxed{0} .

2 Helpful 1 Interesting 0 Brilliant 0 Confused

There is no need for modulus sign!!.Weird problem.

Akash Mandal - 2 years, 2 months ago

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