**Use the discriminant to determine the number of real solutions.**

t2 - 10t + 25 = 0

To determine the number of real solutions for the quadratic equation \( t^2 - 10t + 25 = 0 \), we use the discriminant, which is part of the quadratic formula. The general quadratic equation is \( at^2 + bt + c = 0 \), and the discriminant (\( \Delta \)) is calculated as:

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

For the given equation \( t^2 - 10t + 25 = 0 \), we identify:

- \( a = 1 \)
- \( b = -10 \)
- \( c = 25 \)

Now, substitute these values into the discriminant formula:

\[
\Delta = (-10)^2 - 4(1)(25)
\]
\[
\Delta = 100 - 100 = 0
\]

Since the discriminant is zero (\( \Delta = 0 \)), this means that the quadratic equation has **one real solution**, which is a repeated (or double) root.

### Conclusion:
- The quadratic equation has **exactly one real solution**.

Would you like further details on how the discriminant works, or do you have any questions?

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Here are 5 related questions to further explore the topic:

1. How do you solve quadratic equations using the quadratic formula?
2. What is the geometric meaning of having one real solution in a quadratic equation?
3. Can you find the exact solution for \( t^2 - 10t + 25 = 0 \)?
4. What happens when the discriminant is negative or positive?
5. How can completing the square help solve \( t^2 - 10t + 25 = 0 \)?

**Tip**: The discriminant gives insight into the nature of roots (real and distinct, real and repeated, or complex). Always calculate it before solving quadratics to understand what type of solution you are dealing with!

Use the discriminant to determine the number of real solutions. t^2 - 10t + 25 = 0

Learn how to use the discriminant to determine the number of real solutions for the quadratic equation t^2 - 10t + 25 = 0. This solution covers essential algebraic concepts, including the discriminant formula and its application in analyzing quadratic equations. Suitable for students in Grades 8-10.

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