Find the value of the discriminant of 2x²+5x_-9

The given quadratic equation is:

\[
2x^2 + 5x - 9 = 0
\]

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

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

For the equation \(2x^2 + 5x - 9 = 0\), the coefficients are:
- \(a = 2\)
- \(b = 5\)
- \(c = -9\)

Substituting these values into the discriminant formula:

\[
\Delta = 5^2 - 4(2)(-9)
\]

\[
\Delta = 25 + 72 = 97
\]

So, the value of the discriminant is \(\Delta = 97\).

Would you like details or have any questions? 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 \(b = -5\)?
3. Can you solve the quadratic equation using the quadratic formula?
4. What happens if the discriminant is negative?
5. How can the discriminant help in sketching the graph of a quadratic equation?

**Tip:** A positive discriminant indicates two distinct real roots.

Learn how to find the discriminant of the quadratic equation 2x² + 5x - 9. This problem involves using the discriminant formula Δ = b² - 4ac and covers essential algebraic concepts, including solving quadratic equations. Suitable for students in Grades 8-10.

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