Question

16x^3-12x^2-4=0 помогите найти корни уравнения. с решением

Answer 1

16x³-12x²-4=0
(x-1)(16x²+4x+4)=0
(x-1)=0
x=1
(16x²+4x+4)=0
16х²+4х+4=0
Д=<0 корней нет
Ответ  1

Answer 2

$16x^3 - 12x^2 - 4 = 0$
разделим всё на 4
$4x^3 - 3x^2 - 1 = 0$
заметим, что x = 1 - корень. Тогда разделим всю левую часть на (x-1).
Получаем:
$4x^3 - 3x^2 - 1 = (x - 1)(4x^2 + x + 1)$
решим
$(x - 1)(4x^2 + x + 1) = 0$
x = 1 или $4x^2 + x + 1 = 0$
                     D = 1 - 16 < 0 - решений нет
Ответ: х = 1

Answer 3

Solving the Equation 16x^3 - 12x^2 - 4 = 0

To find the roots of the equation 16x^3 - 12x^2 - 4 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

Where a, b, and c are the coefficients of the equation. Let's calculate the roots using this formula.

Calculating the Roots

First, let's identify the coefficients of the equation: - a = 16 - b = -12 - c = -4

Now, we can use the quadratic formula to find the roots of the equation.

x = (-(-12) ± √((-12)^2 - 4*16*(-4))) / (2*16)

x = (12 ± √(144 + 256)) / 32

x = (12 ± √400) / 32

x = (12 ± 20) / 32

So, the roots of the equation 16x^3 - 12x^2 - 4 = 0 are:

x1 = (12 + 20) / 32 = 32 / 32 = 1

x2 = (12 - 20) / 32 = -8 / 32 = -1/4

Therefore, the roots of the equation are x = 1 and x = -1/4.

Conclusion

The roots of the equation 16x^3 - 12x^2 - 4 = 0 are x = 1 and x = -1/4.