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

To find the discriminant of a quadratic equation in the standard form \( ax^2 + bx + c = 0 \), the discriminant is given by the formula:

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

For the given quadratic equation:

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

Here, the coefficients are:
- \( a = -9 \)
- \( b = -7 \)
- \( c = -7 \)

Now, substitute these values into the discriminant formula:

\[
\Delta = (-7)^2 - 4(-9)(-7)
\]

Calculate it step by step:

1. \( (-7)^2 = 49 \)
2. \( 4 \times (-9) \times (-7) = 4 \times 63 = 252 \)

Thus:

\[
\Delta = 49 - 252 = -203
\]

The discriminant of the quadratic equation is \(\Delta = -203\).

Would you like further details or have any questions?

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Here are 5 related questions you might consider:

1. What does the sign of the discriminant tell you about the roots of a quadratic equation?
2. How can the discriminant help in determining the nature of roots without solving the equation?
3. What happens to the roots if the discriminant is zero?
4. How would the discriminant change if the coefficient \( b \) were positive?
5. How do the coefficients \( a \), \( b \), and \( c \) affect the value of the discriminant?

**Tip:** The discriminant can help quickly determine if a quadratic equation has real or complex roots. If it's negative, the roots are complex.

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

Discover how to calculate the discriminant of the quadratic equation -9x^2 - 7x - 7. This step-by-step solution covers essential algebraic concepts, including the discriminant formula and its application. Ideal for high school students in Grades 9-12.

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