Solve $0=4x^2+12x+9$.Select The Equation That Shows The Correct Substitution Of $a, B,$ And \$c$[/tex\] In The Quadratic Formula.A. $x=\frac{12 \pm \sqrt{12^2-4(4)(9)}}{2(4)}$B. $x=\frac{-12 \pm

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Introduction

Quadratic equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving the quadratic equation $0=4x^2+12x+9$ using the quadratic formula. We will also explore the correct substitution of $a, b,$ and $c$ in the quadratic formula.

Understanding the Quadratic Formula

The quadratic formula is a powerful tool for solving quadratic equations. It is given by:

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

where $a, b,$ and $c$ are the coefficients of the quadratic equation.

Breaking Down the Quadratic Equation

Let's break down the given quadratic equation $0=4x^2+12x+9$. We can see that the coefficients are:

a=4,b=12,c=9a=4, b=12, c=9

Substituting the Coefficients into the Quadratic Formula

Now, let's substitute the coefficients into the quadratic formula:

x=−12±122−4(4)(9)2(4)x=\frac{-12 \pm \sqrt{12^2-4(4)(9)}}{2(4)}

This is the correct substitution of $a, b,$ and $c$ in the quadratic formula.

Comparing the Options

Let's compare the correct substitution with the given options:

A. $x=\frac{12 \pm \sqrt{12^2-4(4)(9)}}{2(4)}$

B. $x=\frac{-12 \pm \sqrt{12^2-4(4)(9)}}{2(4)}$

We can see that option B is the correct substitution of $a, b,$ and $c$ in the quadratic formula.

Solving the Quadratic Equation

Now that we have the correct substitution, let's solve the quadratic equation:

x=−12±122−4(4)(9)2(4)x=\frac{-12 \pm \sqrt{12^2-4(4)(9)}}{2(4)}

x=−12±144−1448x=\frac{-12 \pm \sqrt{144-144}}{8}

x=−12±08x=\frac{-12 \pm \sqrt{0}}{8}

x=−128x=\frac{-12}{8}

x=−32x=-\frac{3}{2}

Therefore, the solution to the quadratic equation $0=4x^2+12x+9$ is $x=-\frac{3}{2}$.

Conclusion

Solving quadratic equations is an essential skill for students to master. In this article, we have focused on solving the quadratic equation $0=4x^2+12x+9$ using the quadratic formula. We have also explored the correct substitution of $a, b,$ and $c$ in the quadratic formula. By following the steps outlined in this article, students can confidently solve quadratic equations and apply the quadratic formula to a wide range of problems.

Frequently Asked Questions

Q: What is the quadratic formula?

A: The quadratic formula is a powerful tool for solving quadratic equations. It is given by:

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

Q: How do I substitute the coefficients into the quadratic formula?

A: To substitute the coefficients into the quadratic formula, simply replace $a, b,$ and $c$ with the corresponding coefficients of the quadratic equation.

Q: What is the correct substitution of $a, b,$ and $c$ in the quadratic formula?

A: The correct substitution of $a, b,$ and $c$ in the quadratic formula is:

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

Q: How do I solve the quadratic equation using the quadratic formula?

A: To solve the quadratic equation using the quadratic formula, simply substitute the coefficients into the formula and simplify the expression.

Additional Resources

For more information on solving quadratic equations, check out the following resources:

  • Khan Academy: Quadratic Equations
  • Mathway: Quadratic Formula
  • Wolfram Alpha: Quadratic Formula

References

  • "Algebra and Trigonometry" by Michael Sullivan
  • "College Algebra" by James Stewart
  • "Quadratic Equations" by Math Open Reference
    Quadratic Equations Q&A: Frequently Asked Questions and Answers ====================================================================

Introduction

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

Q: What is a quadratic equation?

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

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

where $a, b,$ and $c$ are constants.

Q: What is the quadratic formula?

A: The quadratic formula is a powerful tool for solving quadratic equations. It is given by:

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

where $a, b,$ and $c$ are the coefficients of the quadratic equation.

Q: How do I substitute the coefficients into the quadratic formula?

A: To substitute the coefficients into the quadratic formula, simply replace $a, b,$ and $c$ with the corresponding coefficients of the quadratic equation.

Q: What is the correct substitution of $a, b,$ and $c$ in the quadratic formula?

A: The correct substitution of $a, b,$ and $c$ in the quadratic formula is:

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

Q: How do I solve the quadratic equation using the quadratic formula?

A: To solve the quadratic equation using the quadratic formula, simply substitute the coefficients into the formula and simplify the expression.

Q: What is the difference between the quadratic formula and factoring?

A: The quadratic formula and factoring are two different methods for solving quadratic equations. The quadratic formula is a general method that can be used to solve any quadratic equation, while factoring is a specific method that can be used to solve quadratic equations that can be factored.

Q: When should I use the quadratic formula and when should I use factoring?

A: You should use the quadratic formula when:

  • The quadratic equation cannot be factored.
  • The quadratic equation has complex roots.
  • You need to find the roots of a quadratic equation.

You should use factoring when:

  • The quadratic equation can be factored.
  • You need to find the roots of a quadratic equation that can be factored.

Q: How do I determine if a quadratic equation can be factored?

A: To determine if a quadratic equation can be factored, look for two numbers whose product is equal to the constant term (c) and whose sum is equal to the coefficient of the linear term (b).

Q: What is the difference between a quadratic equation and a linear equation?

A: A quadratic equation is a polynomial equation of degree two, while a linear equation is a polynomial equation of degree one.

Q: How do I solve a linear equation?

A: To solve a linear equation, simply isolate the variable (usually x) by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the difference between a quadratic equation and a polynomial equation?

A: A quadratic equation is a polynomial equation of degree two, while a polynomial equation is a general term that refers to any equation that can be written in the form:

anxn+an−1xn−1+…+a1x+a0=0a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0 = 0

where $a_n, a_{n-1}, \ldots, a_1, a_0$ are constants and $n$ is a positive integer.

Conclusion

Quadratic equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we have provided a comprehensive Q&A guide to help students understand and solve quadratic equations. By following the steps outlined in this article, students can confidently solve quadratic equations and apply the quadratic formula to a wide range of problems.

Frequently Asked Questions

Q: What is the quadratic formula?

A: The quadratic formula is a powerful tool for solving quadratic equations. It is given by:

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

Q: How do I substitute the coefficients into the quadratic formula?

A: To substitute the coefficients into the quadratic formula, simply replace $a, b,$ and $c$ with the corresponding coefficients of the quadratic equation.

Q: What is the correct substitution of $a, b,$ and $c$ in the quadratic formula?

A: The correct substitution of $a, b,$ and $c$ in the quadratic formula is:

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

Q: How do I solve the quadratic equation using the quadratic formula?

A: To solve the quadratic equation using the quadratic formula, simply substitute the coefficients into the formula and simplify the expression.

Additional Resources

For more information on solving quadratic equations, check out the following resources:

  • Khan Academy: Quadratic Equations
  • Mathway: Quadratic Formula
  • Wolfram Alpha: Quadratic Formula

References

  • "Algebra and Trigonometry" by Michael Sullivan
  • "College Algebra" by James Stewart
  • "Quadratic Equations" by Math Open Reference