Question

2x^3+12x^2+54x+36=0​

Answer 1

Ответ:

ты не правельно написала или х=0

Answer 2

To solve the equation 2x^3 + 12x^2 + 54x + 36 = 0, we can use the rational root theorem or factorization. However, in this case, the equation can be simplified by dividing both sides by 2 to make the coefficients smaller:

x^3 + 6x^2 + 27x + 18 = 0

Now, let's proceed with finding the roots.

One possible method is to use numerical methods or calculators. However, in this case, the equation can be factored by grouping:

(x^3 + 3x^2) + (3x^2 + 9x) + (18x + 18) = 0 x^2(x + 3) + 3x(x + 3) + 18(x + 1) = 0 (x + 3)(x^2 + 3x + 18) = 0

Now, we have two factors: (x + 3) and (x^2 + 3x + 18). Setting each factor equal to zero and solving for x gives us:

x + 3 = 0 x = -3

x^2 + 3x + 18 = 0

The quadratic equation x^2 + 3x + 18 = 0 does not factor further. We can use the quadratic formula to find its solutions:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 3, and c = 18. Plugging in these values into the quadratic formula:

x = (-3 ± √(3^2 - 4(1)(18))) / (2(1)) x = (-3 ± √(9 - 72)) / 2 x = (-3 ± √(-63)) / 2

Since the discriminant (√(-63)) is negative, the quadratic equation does not have real solutions. Therefore, the only real root of the original equation 2x^3 + 12x^2 + 54x + 36 = 0 is x = -3.