Find the sum of the real roots of the equation x³ + 6x² + 12x + 35 = 0.

Question

Вопрос:

Find the sum of the real roots of the equation x³ + 6x² + 12x + 35 = 0.

Ответ:

ФИО:Телефон:Емаил:Полное описание сути нарушения прав (почему распространение данной информации запрещено Правообладателем):

Accepted Answer

Sum of Roots Problem

Brief Explanation: To find the sum of the real roots of the cubic equation, we can use Vieta's formulas, which relate the coefficients of a polynomial to sums and products of its roots. For a cubic equation of the form ax³ + bx² + cx + d = 0, the sum of the roots is given by -b/a.

Step-by-step solution:

Identify the coefficients: In the given equation, x³ + 6x² + 12x + 35 = 0, we have:
a = 1
b = 6
c = 12
d = 35
Apply Vieta's formulas: According to Vieta's formulas, the sum of the roots (x₁ + x₂ + x₃) is equal to -b/a.
Calculate the sum of the roots:
Sum of roots = -6 / 1 = -6.

Answer: -6