Question

Решение через дискриминант. Помогите пж​

Answer 1

$2x^2+\dfrac{x^2}{|x|}=0\qquad ODZ:\ \ x\ne0\\\\2x^2|x|+x^2=0\\\\\left[\begin{array}{lcl}x\geq 0;\qquad2x^2\cdot x+x^2=0\\x\ \left[\begin{array}{lcl}2x^3+x^2=0\\-2x^3+x^2=0\end{array}$

$\displaystyle 2x^3+x^2=0\\x^2(2x+1)=0\\\\\left[\begin{array}{lcl}x^2=0\\2x+1=0\end{array}\ =>\ \left[\begin{array}{lcl}x=0\\x=-\dfrac12\end{array}$

x = 0 не удовлетворяет ОДЗ

-1/2 не подходит условию x ≥ 0

$-2x^3+x^2=0\\x^2(-2x+1)=0\\\\\left[\begin{array}{lcl}x^2=0\\-2x+1=0\end{array}\ => \ \left[\begin{array}{lcl}x=0\\x=\dfrac12\end{array}$

1/2 не подходит условию x < 0

Ответ:  нет корней

Answer 2

Solving Quadratic Equations Using the Discriminant

To solve a quadratic equation using the discriminant, we need to determine the values of the unknown variable that satisfy the equation. The discriminant is a mathematical expression that helps us determine the nature of the solutions.

The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and x is the unknown variable.

The discriminant, denoted as Δ, is calculated using the formula Δ = b^2 - 4ac. It provides information about the nature of the solutions:

1. If Δ > 0, the equation has two distinct real solutions. 2. If Δ = 0, the equation has one real solution (a repeated root). 3. If Δ < 0, the equation has no real solutions (complex roots).

To find the solutions of the quadratic equation, we can use the quadratic formula: x = (-b ± √Δ) / (2a).

Let's consider an example to illustrate the process.

Example:

Suppose we have the quadratic equation 2x^2 + 5x - 3 = 0. We can find the solutions using the discriminant.

1. Calculate the discriminant: Δ = (5)^2 - 4(2)(-3) = 25 + 24 = 49.

2. Since Δ > 0, the equation has two distinct real solutions.

3. Apply the quadratic formula: x = (-5 ± √49) / (2(2)).

- Solution 1: x = (-5 + 7) / 4 = 2 / 4 = 0.5. - Solution 2: x = (-5 - 7) / 4 = -12 / 4 = -3.

Therefore, the solutions to the quadratic equation 2x^2 + 5x - 3 = 0 are x = 0.5 and x = -3.

Please note that this is just one example, and the process remains the same for any quadratic equation.

I hope this explanation helps! Let me know if you have any further questions.