Question

25x+20x²+4x³=0 срочно​

Answer 1

Ответ:

$x_1 = 0 \\ x_2 = - 2.5$

$25x + 20 {x}^{2} + 4 {x}^{3} = 0 \\ x(4 {x}^{2} + 20x + 25) = 0$

произведение равно нулю когда один из множителей равен нулю:

$x1 = 0$

или

$4 {x}^{2} + 20x + 25 = 0 \\ \\ D = {b}^{2} - 4 ac = {20}^{2} - 4 \times 4 \times 25 = 400 - 400 = 0 \\ \\ x_2 = \dfrac{ - b}{2a} = \dfrac{ - 20}{2 \times 4} = - \dfrac{20}{8} = - \frac{5}{2} = - 2.5$

Answer 2

Solving the Equation 25x + 20x² + 4x³ = 0

To solve the equation 25x + 20x² + 4x³ = 0, we can use various methods such as factoring, the quadratic formula, or the cubic formula. Let's start by factoring the equation.

Factoring the Equation

First, let's factor out the common term 'x' from each term: 25x + 20x² + 4x³ = x(25 + 20x + 4x²)

Now, we can factor the quadratic expression inside the parentheses: 25 + 20x + 4x² = (5 + 2x)(5 + 2x)

So, the factored form of the equation becomes: x(5 + 2x)(5 + 2x) = 0

Finding the Solutions

Now, we can find the solutions by setting each factor equal to zero: 1. x = 0 2. 5 + 2x = 0 3. 5 + 2x = 0

Solving for x in the second and third equations: 2x = -5 x = -5/2

So, the solutions to the equation 25x + 20x² + 4x³ = 0 are: x = 0, x = -5/2

These are the real solutions to the given equation.