Find the discriminant value and determine the nature of 2x²-10x+8=0

To find the discriminant of a quadratic equation and determine its nature, we use the following formula:

\[
\text{Discriminant} = \Delta = b^2 - 4ac
\]

Given the quadratic equation: 

\[
2x^2 - 10x + 8 = 0
\]

Here, \(a = 2\), \(b = -10\), and \(c = 8\).

### Step 1: Calculate the Discriminant
\[
\Delta = (-10)^2 - 4(2)(8)
\]
\[
\Delta = 100 - 64
\]
\[
\Delta = 36
\]

### Step 2: Determine the Nature of the Roots
- If \(\Delta > 0\), the equation has **two distinct real roots**.
- If \(\Delta = 0\), the equation has **one real root (a repeated root)**.
- If \(\Delta < 0\), the equation has **two complex roots**.

Since \(\Delta = 36 > 0\), the quadratic equation has **two distinct real roots**.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How do you calculate the roots of the quadratic equation using the quadratic formula?
2. What happens to the discriminant if the quadratic equation is modified?
3. How can you identify the vertex of a parabola from a quadratic equation?
4. Can you find the axis of symmetry for the given quadratic equation?
5. What is the sum and product of the roots of this equation?

**Tip:** The discriminant not only tells you the nature of the roots but also gives insight into how the parabola behaves on a graph!

Learn how to find the discriminant of the quadratic equation 2x² - 10x + 8 = 0 and determine the nature of its roots. This problem covers the calculation of the discriminant and its implications on the nature of quadratic roots, including two distinct real roots. Suitable for advanced high school students (Grades 10-12).

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