Find the discriminant and nature of x²+5x+10=0

To find the discriminant of the quadratic equation \(x^2 + 5x + 10 = 0\), we use the formula for the discriminant:

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

Where:
- \(a = 1\) (coefficient of \(x^2\)),
- \(b = 5\) (coefficient of \(x\)),
- \(c = 10\) (constant term).

Now, substituting these values into the discriminant formula:

\[
\Delta = (5)^2 - 4(1)(10) = 25 - 40 = -15
\]

### Nature of the roots:
Since the discriminant \(\Delta = -15\) is **negative**, the quadratic equation has:
- **No real roots**,
- **Two complex (conjugate) roots**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do complex roots look for quadratic equations with a negative discriminant?
2. Can you calculate the roots for \(x^2 + 5x + 10 = 0\)?
3. How does the discriminant determine the nature of roots?
4. What happens when the discriminant is zero or positive?
5. How do we factor quadratic equations with real roots?

**Tip:** The discriminant tells you whether a quadratic equation has real or complex roots!

Learn how to find the discriminant and determine the nature of the roots for the quadratic equation x² + 5x + 10 = 0. This problem covers key algebraic concepts, including the discriminant formula and the nature of roots theorem, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation