State the value of the discriminant for the equation.

 

−10x2−3x+2

The given quadratic equation is:

\[
-10x^2 - 3x + 2 = 0
\]

The discriminant \( \Delta \) of a quadratic equation \( ax^2 + bx + c = 0 \) is given by the formula:

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

For the equation \( -10x^2 - 3x + 2 = 0 \), we can identify the coefficients as:
- \( a = -10 \)
- \( b = -3 \)
- \( c = 2 \)

Substitute these values into the discriminant formula:

\[
\Delta = (-3)^2 - 4(-10)(2)
\]

Now, calculate step by step:

\[
\Delta = 9 - 4(-10)(2)
\]
\[
\Delta = 9 - (-80)
\]
\[
\Delta = 9 + 80 = 89
\]

Thus, the discriminant is \( \Delta = 89 \).

Would you like more details or any clarifications?

---

Here are 5 related questions:
1. What does the discriminant tell us about the nature of the roots?
2. How would the discriminant change if \( c = 3 \)?
3. Can you solve for the roots of this quadratic equation using the quadratic formula?
4. What happens to the discriminant if the equation's leading coefficient \( a \) is doubled?
5. How does the discriminant affect the graph of the quadratic function?

**Tip:** The sign of the discriminant indicates the nature of the roots: positive for two real roots, zero for one real root, and negative for complex roots.

State the value of the discriminant for the equation −10x^2−3x+2.

Learn how to find the discriminant for the quadratic equation −10x^2−3x+2. This solution explains step-by-step how to use the discriminant formula Δ = b^2 - 4ac to determine the value of Δ, with key algebraic concepts and examples. Suitable for 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