2 x sqaure minus 5 x plus 6 =0 Solve this

The given equation is a quadratic equation in the form:

\[
2x^2 - 5x + 6 = 0
\]

To solve this quadratic equation, we can use the **quadratic formula**:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

For the given equation \( 2x^2 - 5x + 6 = 0 \), the coefficients are:
- \( a = 2 \)
- \( b = -5 \)
- \( c = 6 \)

Now, substitute these values into the quadratic formula:

\[
x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(2)(6)}}{2(2)}
\]

Simplifying:

\[
x = \frac{5 \pm \sqrt{25 - 48}}{4}
\]
\[
x = \frac{5 \pm \sqrt{-23}}{4}
\]

Since the discriminant \( 25 - 48 = -23 \) is negative, the equation has **no real solutions**. However, it has **complex solutions**. We can express the result as:

\[
x = \frac{5 \pm \sqrt{23}i}{4}
\]

Thus, the solutions are:

\[
x = \frac{5 + \sqrt{23}i}{4} \quad \text{and} \quad x = \frac{5 - \sqrt{23}i}{4}
\]

These are the two complex solutions.

Would you like more details on the steps or have any questions?

Here are 5 related questions:
1. What does it mean when the discriminant is negative?
2. How do you solve quadratic equations with real roots?
3. What is the significance of complex numbers in equations?
4. Can quadratic equations have more than two solutions?
5. What are some practical applications of quadratic equations?

**Tip:** Always check the discriminant \((b^2 - 4ac)\) to quickly determine the nature of the roots—real or complex!

2 x square minus 5 x plus 6 = 0 Solve this

Learn how to solve the quadratic equation 2x^2 - 5x + 6 = 0. This step-by-step guide covers the quadratic formula and how to find complex solutions when the discriminant is negative. Ideal for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation