Which Shows The Equation Below Written In The Form $a X^2+b X+c=0$?$2 X^2-3=-4 X-1$A. \$2 X^2-4 X-4=0$[/tex\] B. $2 X^2-4 X-2=0$ C. $2 X^2+4 X-4=0$ D. \$2 X^2+4 X-2=0$[/tex\]

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Introduction

Quadratic equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will explore how to rewrite a given quadratic equation in the standard form ax2+bx+c=0ax^2 + bx + c = 0. We will use a step-by-step approach to solve the equation and provide a clear understanding of the process.

Understanding the Equation

The given equation is:

2x2−3=−4x−12x^2 - 3 = -4x - 1

Our goal is to rewrite this equation in the standard form ax2+bx+c=0ax^2 + bx + c = 0. To do this, we need to isolate the terms with xx on one side of the equation.

Step 1: Move the Constant Terms to the Right Side

The first step is to move the constant terms to the right side of the equation. We can do this by adding 4x+14x + 1 to both sides of the equation.

2x2−3+4x+1=−4x−1+4x+12x^2 - 3 + 4x + 1 = -4x - 1 + 4x + 1

Simplifying the equation, we get:

2x2+4x−2=02x^2 + 4x - 2 = 0

Step 2: Identify the Coefficients

Now that we have the equation in the standard form, we can identify the coefficients aa, bb, and cc. In this case, a=2a = 2, b=4b = 4, and c=−2c = -2.

Step 3: Write the Equation in the Standard Form

Using the coefficients we identified in the previous step, we can write the equation in the standard form:

2x2+4x−2=02x^2 + 4x - 2 = 0

Conclusion

In this article, we have shown how to rewrite a given quadratic equation in the standard form ax2+bx+c=0ax^2 + bx + c = 0. We used a step-by-step approach to solve the equation and provided a clear understanding of the process. By following these steps, you can easily rewrite any quadratic equation in the standard form.

Answer

Based on the steps we followed, the correct answer is:

  • B. 2x2−4x−2=02x^2 - 4x - 2 = 0

However, we made a mistake in the equation. The correct answer is:

  • B. 2x2+4x−2=02x^2 + 4x - 2 = 0

Comparison of Options

Let's compare the options we were given:

  • A. 2x2−4x−4=02x^2 - 4x - 4 = 0: This option is incorrect because the coefficient of xx is negative, whereas in our solution, it is positive.
  • B. 2x2+4x−2=02x^2 + 4x - 2 = 0: This option is correct because it matches the equation we derived in the previous steps.
  • C. 2x2+4x−4=02x^2 + 4x - 4 = 0: This option is incorrect because the constant term is different from the one we derived.
  • D. 2x2+4x−2=02x^2 + 4x - 2 = 0: This option is incorrect because the coefficient of xx is positive, whereas in our solution, it is negative.

Final Answer

The final answer is:

  • B. 2x2+4x−2=02x^2 + 4x - 2 = 0
    Quadratic Equations: A Q&A Guide =====================================

Introduction

Quadratic equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will provide a Q&A guide to help you understand quadratic equations and how to solve them.

Q: What is a Quadratic Equation?

A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable (usually x) is two. It is written in the form:

ax2+bx+c=0ax^2 + bx + c = 0

where a, b, and c are constants.

Q: How Do I Solve a Quadratic Equation?

To solve a quadratic equation, you can use the following steps:

  1. Move the constant terms to the right side: Move all the constant terms to the right side of the equation.
  2. Identify the coefficients: Identify the coefficients a, b, and c.
  3. Write the equation in the standard form: Write the equation in the standard form ax2+bx+c=0ax^2 + bx + c = 0.

Q: What is the Standard Form of a Quadratic Equation?

The standard form of a quadratic equation is:

ax2+bx+c=0ax^2 + bx + c = 0

where a, b, and c are constants.

Q: How Do I Identify the Coefficients?

To identify the coefficients, you need to look at the equation and identify the values of a, b, and c. For example, in the equation:

2x2+4x−2=02x^2 + 4x - 2 = 0

the coefficients are:

  • a = 2
  • b = 4
  • c = -2

Q: What is the Difference Between a Quadratic Equation and a Linear Equation?

A quadratic equation is a polynomial equation of degree two, while a linear equation is a polynomial equation of degree one. In other words, a quadratic equation has a squared variable (x^2), while a linear equation does not.

Q: Can I Use a Calculator to Solve a Quadratic Equation?

Yes, you can use a calculator to solve a quadratic equation. Most calculators have a built-in quadratic equation solver that can help you find the solutions.

Q: What is the Formula for Solving a Quadratic Equation?

The formula for solving a quadratic equation is:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

This formula is known as the quadratic formula.

Q: How Do I Use the Quadratic Formula?

To use the quadratic formula, you need to plug in the values of a, b, and c into the formula. For example, if you have the equation:

2x2+4x−2=02x^2 + 4x - 2 = 0

you can plug in the values:

  • a = 2
  • b = 4
  • c = -2

into the formula:

x=−4±42−4(2)(−2)2(2)x = \frac{-4 \pm \sqrt{4^2 - 4(2)(-2)}}{2(2)}

Simplifying the equation, you get:

x=−4±16+164x = \frac{-4 \pm \sqrt{16 + 16}}{4}

x=−4±324x = \frac{-4 \pm \sqrt{32}}{4}

x=−4±424x = \frac{-4 \pm 4\sqrt{2}}{4}

x=−4±424x = \frac{-4 \pm 4\sqrt{2}}{4}

x=−1±2x = -1 \pm \sqrt{2}

Conclusion

In this article, we have provided a Q&A guide to help you understand quadratic equations and how to solve them. We have covered topics such as the standard form of a quadratic equation, identifying coefficients, and using the quadratic formula. By following these steps, you can easily solve quadratic equations and become proficient in this important mathematical concept.

Final Answer

The final answer is:

  • B. 2x2+4x−2=02x^2 + 4x - 2 = 0