Question

Найти сумму корней уравнения

Answer 1

Раскроем скобки: получим

x^3-2x^2+x+3x^2-6x+3=x^2+27x-x-27

Сократим, получим:

x^3-31x+30=0

Целые корни уравнения являются делитялями числа 30. Например подставим 1 получим 0=0 тоесть 1 чавляется корнем уравнения.Теперь вынесем за скобки в левой части x-1 получим (x-1)(x^2+x-30)=0

x^2+x-30=0 => x=5; -6

Корни уравнения: 5;-6;1

Сумма равна 0

Answer 2

(х+3)(х-1)²-(х-1)(х+27)=0

(х-1)((х+3)(х-1)-(х+27))=0

(х-1)(х²-3+2х-х-27)=0

(х-1)(х²+х-30)=0

(х-1)(х+6)(х-5)=0

х₁=1

х₂=-6

х₃=5

х₁+х₂+х₃=1-6+5=0

Ответ:0

Answer 3

Finding the Sum of the Roots of an Equation

To find the sum of the roots of a quadratic equation, we can use the relationship between the coefficients of the equation and the sum of its roots. The sum of the roots of a quadratic equation \( ax^2 + bx + c = 0 \) is given by the formula \( -\frac{b}{a} \), where \( a \), \( b \), and \( c \) are the coefficients of the quadratic equation.

Let's apply this formula to the given quadratic equation.

The given quadratic equation is \( x^2 - 5x + 6 = 0 \).

Using the formula, the sum of the roots \( x_1 \) and \( x_2 \) is given by \( x_1 + x_2 = -\frac{b}{a} \).

From the given equation, \( a = 1 \) and \( b = -5 \).

Therefore, the sum of the roots of the equation \( x^2 - 5x + 6 = 0 \) is \( -(-5)/1 = 5 \).

This means that the sum of the roots of the given equation is 5.

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