Determine The Discriminant For The Quadratic Equation 0 = − 2 X 2 + 3 0 = -2x^2 + 3 0 = − 2 X 2 + 3 . Based On The Discriminant Value, How Many Real Number Solutions Does The Equation Have?Discriminant = B 2 − 4 A C = B^2 - 4ac = B 2 − 4 A C A. 0 B. 1 C. 2 D. 24

Mar 13, 2025 by ADMIN 266 views

**Determining the Discriminant for a Quadratic Equation**

Introduction

In algebra, a quadratic equation is a polynomial equation of degree two, which means the highest power of the variable is two. The general form of a quadratic equation is $ax^2 + bx + c = 0$ , where $a$ , $b$ , and $c$ are constants, and $x$ is the variable. The discriminant of a quadratic equation is a value that can be calculated from the coefficients of the equation and is used to determine the nature of the solutions. In this article, we will determine the discriminant for the quadratic equation $0 = -2x^2 + 3$ and use it to find out how many real number solutions the equation has.

Understanding the Quadratic Equation

The given quadratic equation is $0 = -2x^2 + 3$ . To determine the discriminant, we need to identify the coefficients $a$ , $b$ , and $c$ . In this equation, $a = -2$ , $b = 0$ , and $c = 3$ . The discriminant is given by the formula $b^2 - 4ac$ .

Calculating the Discriminant

Using the formula for the discriminant, we can calculate the value as follows:

$b^2 - 4ac = 0^2 - 4(-2)(3) = 0 - (-24) = 24$

Therefore, the discriminant of the quadratic equation $0 = -2x^2 + 3$ is $24$ .

Interpreting the Discriminant Value

The discriminant value can be used to determine the nature of the solutions of the quadratic equation. If the discriminant is positive, the equation has two distinct real number solutions. If the discriminant is zero, the equation has one real number solution. If the discriminant is negative, the equation has no real number solutions.

In this case, the discriminant value is $24$ , which is positive. Therefore, the quadratic equation $0 = -2x^2 + 3$ has two distinct real number solutions.

Conclusion

In conclusion, we have determined the discriminant for the quadratic equation $0 = -2x^2 + 3$ and used it to find out how many real number solutions the equation has. The discriminant value is $24$ , which indicates that the equation has two distinct real number solutions.

Final Answer

The final answer is $\boxed{2}$ .

Additional Information

For those who are interested in learning more about quadratic equations and discriminants, here are some additional resources:

References

Math Is Fun
Math Open Reference
Khan Academy
Quadratic Equation Discriminant Q&A =====================================

Introduction

In our previous article, we discussed how to determine the discriminant for a quadratic equation and used it to find out how many real number solutions the equation has. In this article, we will answer some frequently asked questions about quadratic equation discriminants.

Q: What is the discriminant of a quadratic equation?

A: The discriminant of a quadratic equation is a value that can be calculated from the coefficients of the equation and is used to determine the nature of the solutions. It is given by the formula $b^2 - 4ac$ .

Q: How do I calculate the discriminant of a quadratic equation?

A: To calculate the discriminant, you need to identify the coefficients $a$ , $b$ , and $c$ of the quadratic equation. Then, you can use the formula $b^2 - 4ac$ to calculate the discriminant.

Q: What does the discriminant value indicate?

A: The discriminant value can be used to determine the nature of the solutions of the quadratic equation. If the discriminant is positive, the equation has two distinct real number solutions. If the discriminant is zero, the equation has one real number solution. If the discriminant is negative, the equation has no real number solutions.

Q: How do I determine the number of real number solutions of a quadratic equation?

A: To determine the number of real number solutions of a quadratic equation, you need to calculate the discriminant and use it to determine the nature of the solutions. If the discriminant is positive, the equation has two distinct real number solutions. If the discriminant is zero, the equation has one real number solution. If the discriminant is negative, the equation has no real number solutions.

Q: What is the difference between a quadratic equation with two distinct real number solutions and one with one real number solution?

A: A quadratic equation with two distinct real number solutions has two distinct values of $x$ that satisfy the equation. On the other hand, a quadratic equation with one real number solution has only one value of $x$ that satisfies the equation.

Q: Can a quadratic equation have no real number solutions?

A: Yes, a quadratic equation can have no real number solutions. This occurs when the discriminant is negative.

Q: How do I graph a quadratic equation with two distinct real number solutions?

A: To graph a quadratic equation with two distinct real number solutions, you need to find the $x$ -intercepts of the equation. The $x$ -intercepts are the values of $x$ that satisfy the equation. You can then use these values to graph the equation.

Q: How do I graph a quadratic equation with one real number solution?

A: To graph a quadratic equation with one real number solution, you need to find the $x$ -intercept of the equation. The $x$ -intercept is the value of $x$ that satisfies the equation. You can then use this value to graph the equation.

Q: Can a quadratic equation have complex number solutions?

A: Yes, a quadratic equation can have complex number solutions. This occurs when the discriminant is negative.

Conclusion

In conclusion, we have answered some frequently asked questions about quadratic equation discriminants. We hope that this article has provided you with a better understanding of quadratic equation discriminants and how to use them to determine the nature of the solutions.

Additional Information

For those who are interested in learning more about quadratic equations and discriminants, here are some additional resources: