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The given quadratic equation is:

\[
x^2 - 7x + 5 = 0
\]

We are asked to determine the type of solutions it has. To classify the roots of a quadratic equation, we can use the **discriminant** formula, which is derived from the quadratic formula:

\[
\text{Discriminant} = b^2 - 4ac
\]

For a general quadratic equation \( ax^2 + bx + c = 0 \), the discriminant will tell us the nature of the roots as follows:
- If the discriminant is positive, the equation has two distinct real solutions.
- If the discriminant is zero, the equation has exactly one real solution (a repeated root).
- If the discriminant is negative, the equation has two distinct complex (imaginary) solutions.

For the equation \( x^2 - 7x + 5 = 0 \):
- \( a = 1 \)
- \( b = -7 \)
- \( c = 5 \)

Let's calculate the discriminant.The discriminant for the quadratic equation \( x^2 - 7x + 5 = 0 \) is 29. 

Since the discriminant is positive, this means the equation has **two distinct real solutions**.

Thus, the correct option is:

① 異なる2つの実数解をもつ (Two distinct real solutions).

Would you like further details or clarifications?

Here are 5 related questions:
1. What are the actual solutions of the quadratic equation \(x^2 - 7x + 5 = 0\)?
2. How can we solve quadratic equations using the quadratic formula?
3. What does it mean when the discriminant is zero or negative?
4. Can the discriminant be applied to cubic or higher-order equations?
5. How do complex (imaginary) solutions appear in real-life applications?

**Tip:** Always check the sign of the discriminant to classify the roots of a quadratic equation before solving it!

Determine the type of solution for the quadratic equation: x^2 - 7x + 5 = 0.

Learn how to solve the quadratic equation x^2 - 7x + 5 and determine the nature of its solutions by calculating the discriminant. This problem explains whether the equation has real or imaginary roots. Suitable for students in Grades 8-10.

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