What is the discriminant of the quadratic equation minus, 6, x, squared, plus, 9, x, minus, 7, equals, 0−6*x*2+9*x*−7=0?

The quadratic equation you provided is:

\[
-6x^2 + 9x - 7 = 0
\]

To find the discriminant of a quadratic equation, we use the formula:

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

For the equation in the form \( ax^2 + bx + c = 0 \), we identify:
- \( a = -6 \)
- \( b = 9 \)
- \( c = -7 \)

Now, substitute these values into the discriminant formula:

\[
\Delta = 9^2 - 4(-6)(-7)
\]
\[
\Delta = 81 - 4(42)
\]
\[
\Delta = 81 - 168
\]
\[
\Delta = -87
\]

So, the discriminant is:

\[
\Delta = -87
\]

### Do you want more details or have any questions?

Here are some related questions:
1. What does a negative discriminant imply about the nature of the roots?
2. How do we solve quadratic equations with a negative discriminant?
3. What are the possible types of solutions based on the value of the discriminant?
4. Can you solve the quadratic equation using the quadratic formula?
5. How is the discriminant used in determining the vertex of a parabola?

**Tip:** A negative discriminant indicates that the quadratic equation has two complex (non-real) solutions.

What is the discriminant of the quadratic equation -6*x^2 + 9*x - 7 = 0?

Learn how to find the discriminant of the quadratic equation -6x^2 + 9x - 7. This step-by-step guide explains the discriminant formula, key algebraic concepts, and how the discriminant determines the nature of the roots. Ideal for students in Grades 8-10.

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