Question

Розв'яжіть рівняння : х^3+6x^2+2x+12+0. ОЧЕНЬ СРОЧНО, ОТДАМ 10 балов

Answer 1

Ответ:

x = -6

Объяснение:

x³ + 6x² + 2x + 12 = 0

x²(x + 6) + 2(x + 6) = 0

(x + 6)(x² + 2) = 0

x² + 2 > 0, значит 2-я скобка решений не дает!

x + 6 = 0

x = -6

Answer 2

The translation of your message from Ukrainian to English is:

Answer in detail. Solve the equation: x^3 + 6x^2 + 2x + 12 = 0. VERY URGENT, I WILL GIVE 10 points.

To solve this equation, we can use the rational root theorem, which states that if a polynomial equation with integer coefficients has a rational root, then it must be a divisor of the constant term. In this case, the constant term is 12, so the possible rational roots are ±1, ±2, ±3, ±4, ±6, and ±12. We can use synthetic division to test each of these roots until we find one that gives a zero remainder. For example, let us try x = -2:

-2 | 1 6 2 12 | -2 -8 -12 |--------------- | 1 4 -6 0

Since the remainder is zero, x = -2 is a root of the equation. This means that we can factor out (x + 2) from the polynomial, and get:

x^3 + 6x^2 + 2x + 12 = (x + 2)(x^2 + 4x - 6)

Now, we can use the quadratic formula to find the other two roots of the equation:

x = (-4 ± √(16 + 24))/2 x = (-4 ± √40)/2 x = (-4 ± 2√10)/2 x = -2 ± √10

Therefore, the three roots of the equation are x = -2, x = -2 + √10, and x = -2 - √10. You can check these answers by plugging them back into the original equation and verifying that they make it equal to zero. I hope this helps you understand how to solve this equation. If you need more help, you can use the online calculators from the web search results .