What Is The Product Of The Two Values Of $x$ That Satisfy The Following Equation?$x^2 + 5x + 4 = 0$A. -4 B. -5 C. 5 D. 4 E. 0

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Introduction

In this article, we will explore the concept of solving quadratic equations and finding the product of the two values of x that satisfy a given equation. We will use the quadratic equation x2+5x+4=0x^2 + 5x + 4 = 0 as an example to demonstrate the steps involved in solving the equation and finding the product of the two values of x.

Understanding Quadratic Equations

A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable (in this case, x) is two. The general form of a quadratic equation is ax2+bx+c=0ax^2 + bx + c = 0, where a, b, and c are constants. In our example, the equation is x2+5x+4=0x^2 + 5x + 4 = 0, where a = 1, b = 5, and c = 4.

Solving the Quadratic Equation

To solve the quadratic equation, we can use the quadratic formula, which is given by:

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

In our example, we have a = 1, b = 5, and c = 4. Plugging these values into the quadratic formula, we get:

x=−5±52−4(1)(4)2(1)x = \frac{-5 \pm \sqrt{5^2 - 4(1)(4)}}{2(1)}

Simplifying the expression under the square root, we get:

x=−5±25−162x = \frac{-5 \pm \sqrt{25 - 16}}{2}

x=−5±92x = \frac{-5 \pm \sqrt{9}}{2}

x=−5±32x = \frac{-5 \pm 3}{2}

This gives us two possible values of x:

x1=−5+32=−1x_1 = \frac{-5 + 3}{2} = -1

x2=−5−32=−4x_2 = \frac{-5 - 3}{2} = -4

Finding the Product of the Two Values of x

Now that we have found the two values of x that satisfy the equation, we need to find their product. The product of two numbers is obtained by multiplying them together. In this case, we need to multiply x1 and x2:

x1×x2=(−1)×(−4)=4x_1 \times x_2 = (-1) \times (-4) = 4

Therefore, the product of the two values of x that satisfy the equation is 4.

Conclusion

In this article, we have demonstrated how to solve a quadratic equation and find the product of the two values of x that satisfy the equation. We used the quadratic formula to find the two values of x and then multiplied them together to find their product. The product of the two values of x is 4, which is the correct answer.

Frequently Asked Questions

  • What is a quadratic equation? A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable (in this case, x) is two.
  • How do I solve a quadratic equation? You can use the quadratic formula to solve a quadratic equation. The quadratic formula is given by: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
  • What is the product of the two values of x that satisfy the equation? The product of the two values of x that satisfy the equation is obtained by multiplying them together.

References

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Introduction

In our previous article, we explored the concept of solving quadratic equations and finding the product of the two values of x that satisfy a given equation. In this article, we will answer some of the most frequently asked questions about quadratic equations.

Q&A

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 (in this case, x) is two. The general 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 solve a quadratic equation?

A: You can use the quadratic formula to solve a quadratic equation. The quadratic formula is given by:

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

Q: What is the quadratic formula?

A: The quadratic formula is a mathematical formula that is used to solve quadratic equations. It is given by:

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

Q: How do I find the product of the two values of x that satisfy a quadratic equation?

A: To find the product of the two values of x that satisfy a quadratic equation, you can multiply the two values of x together.

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. In other words, a quadratic equation has a highest power of two, while a linear equation has a highest power of one.

Q: Can I solve a quadratic equation by factoring?

A: Yes, you can solve a quadratic equation by factoring. However, not all quadratic equations can be factored, and the quadratic formula is a more general method for solving quadratic equations.

Q: What is the discriminant in the quadratic formula?

A: The discriminant is the expression under the square root in the quadratic formula, which is given by b2−4acb^2 - 4ac. If the discriminant is positive, the quadratic equation has two distinct real solutions. If the discriminant is zero, the quadratic equation has one real solution. If the discriminant is negative, the quadratic equation has no real solutions.

Q: Can I use a calculator to solve a quadratic equation?

A: Yes, you can use a calculator to solve a quadratic equation. Many calculators have a built-in quadratic formula function that you can use to solve quadratic equations.

Conclusion

In this article, we have answered some of the most frequently asked questions about quadratic equations. We hope that this article has been helpful in clarifying any confusion you may have had about quadratic equations.

Frequently Asked Questions

  • What is a quadratic equation?
  • How do I solve a quadratic equation?
  • What is the quadratic formula?
  • How do I find the product of the two values of x that satisfy a quadratic equation?
  • What is the difference between a quadratic equation and a linear equation?
  • Can I solve a quadratic equation by factoring?
  • What is the discriminant in the quadratic formula?
  • Can I use a calculator to solve a quadratic equation?

References

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