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

Let's solve the quadratic equation \( 2x^2 - 10x + 8 = 0 \).

### Step 1: Identify the coefficients
The general form of a quadratic equation is:

\[
ax^2 + bx + c = 0
\]

Here, comparing this with \( 2x^2 - 10x + 8 = 0 \), we have:
- \( a = 2 \)
- \( b = -10 \)
- \( c = 8 \)

### Step 2: Find the Discriminant
The discriminant \( \Delta \) is given by the formula:

\[
\Delta = b^2 - 4ac
\]

Substitute the values of \( a \), \( b \), and \( c \):

\[
\Delta = (-10)^2 - 4(2)(8) = 100 - 64 = 36
\]

### Step 3: Determine the Nature of the Roots
The nature of the roots depends on the discriminant value:
- If \( \Delta > 0 \), the equation has **two distinct real roots**.
- If \( \Delta = 0 \), the equation has **exactly one real root (a repeated root)**.
- If \( \Delta < 0 \), the equation has **two complex conjugate roots**.

Here, \( \Delta = 36 \), which is greater than 0, so the quadratic equation has **two distinct real roots**.

### Summary
- Discriminant \( \Delta = 36 \)
- The quadratic equation has **two distinct real roots**.

Would you like further details on how to find these roots or have any additional questions?

Here are 5 related questions:
1. How do you calculate the exact roots using the quadratic formula?
2. What does it mean if the discriminant were zero?
3. How is the discriminant derived from the quadratic equation?
4. Can the discriminant help in factoring the quadratic equation?
5. What are some real-world applications of solving quadratic equations?

**Tip:** Always check the discriminant first when solving quadratic equations—it gives valuable information about the nature of the roots.

Learn how to find the discriminant value and determine the nature of the roots for the quadratic equation 2x² - 10x + 8 = 0. Discover the discriminant formula and understand its implications in solving quadratic equations. Suitable for Grades 9-12.

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