It is a question from quadratic equations

Please solve it as early as possible

Let's dive into solving a quadratic equation together! A quadratic equation typically takes the form of ax² + bx + c = 0, where a, b, and c are constants, and a is not equal to zero. To illustrate the solution process, let’s consider a specific example: 2x² + 4x - 6 = 0.

Step 1: Identify the Coefficients

In our equation, we can identify the coefficients as follows:

• a = 2
• b = 4
• c = -6

Step 2: Apply the Quadratic Formula

The quadratic formula is a powerful tool for finding the roots of any quadratic equation. It is given by:

x = (-b ± √(b² - 4ac)) / (2a)

Now, let's plug in our coefficients into this formula.

Step 3: Calculate the Discriminant

The discriminant (D) is the part of the formula under the square root: D = b² - 4ac. This value helps us determine the nature of the roots.

For our equation:

• D = 4² - 4(2)(-6)
• D = 16 + 48
• D = 64

Since the discriminant is positive, we will have two distinct real roots.

Step 4: Solve for x

Now, we can substitute the values of a, b, and D back into the quadratic formula:

• x = (-4 ± √64) / (2 * 2)
• x = (-4 ± 8) / 4

This gives us two possible solutions:

• x₁ = (-4 + 8) / 4 = 4 / 4 = 1
• x₂ = (-4 - 8) / 4 = -12 / 4 = -3

Final Solutions

The solutions to the quadratic equation 2x² + 4x - 6 = 0 are:

• x = 1
• x = -3

In summary, we identified the coefficients, applied the quadratic formula, calculated the discriminant, and found the roots. This method can be applied to any quadratic equation, making it a versatile tool in algebra. If you have any more questions or need further clarification, feel free to ask!