Question

Помогите пожалуйста решить пример.Очень нужно!!!!x^3-7x+6=0. Если можно с объяснением.Ответ должен получиться 2, т.к. в ответ нужно записать больший корень.

Answer 1

Угадываем корень x=2. Теперь преобразуем многочлен так, чтобы выделялся множитель х-2.
x^3-7x+6=(x^3-2x^2)+(2x^2-4x)-(3x-6)=x^2(x-2)+2x(x-2)-3(x-2)=(x-2)(x^2+2x-3).
Решаем квадратное уравнение x^2+2x-3=0. По т. Виета находим еще два корня: -3 и 1. Итак, ответ: -3, 1, 2.

Answer 2

Solving the Equation x^3 - 7x + 6 = 0

To solve the equation x^3 - 7x + 6 = 0 and find the value of x, we can use the Rational Root Theorem and synthetic division to factorize the polynomial and find its roots.

The Rational Root Theorem states that if a polynomial equation has a rational root, then that root will be a factor of the constant term divided by a factor of the leading coefficient. In this case, the constant term is 6, and the leading coefficient is 1.

Using synthetic division, we can test potential rational roots to find the actual roots of the polynomial equation.

Let's proceed with the solution.

Solution Steps

1. Potential Rational Roots: The potential rational roots of the equation x^3 - 7x + 6 = 0 can be found by considering the factors of the constant term (6) and the leading coefficient (1). The potential rational roots are ±1, ±2, ±3, and ±6.

2. Synthetic Division: We will use synthetic division to test these potential rational roots and find the actual roots of the polynomial equation.

3. Finding the Roots: By testing the potential rational roots using synthetic division, we can find the actual roots of the polynomial equation.

Solution Using Synthetic Division

Let's use synthetic division to test the potential rational roots and find the actual roots of the polynomial equation x^3 - 7x + 6 = 0.

We will start by testing the potential rational root x = 1.

Performing synthetic division for x = 1: ``` 1 | 1 0 -7 6 | 1 1 -6 | 1 1 -6 0 ``` The remainder is 0, which means that x = 1 is a root of the polynomial equation.

Now, we have factored the polynomial as (x - 1)(x^2 + x - 6) = 0.

Factoring the quadratic equation x^2 + x - 6 = 0 gives us (x - 1)(x + 3)(x - 2) = 0.

So, the roots of the polynomial equation x^3 - 7x + 6 = 0 are x = 1, x = -3, and x = 2.

Conclusion

The roots of the polynomial equation x^3 - 7x + 6 = 0 are x = 1, x = -3, and x = 2. Therefore, the larger root is 2.