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To solve the question, we need to find the discriminant of the quadratic equation \( x^2 - 5x + 3 = 0 \).

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

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

In this case, comparing \( x^2 - 5x + 3 = 0 \) to the general form \( ax^2 + bx + c = 0 \):

- \( a = 1 \)
- \( b = -5 \)
- \( c = 3 \)

Now, applying the values in the discriminant formula:

\[
\Delta = (-5)^2 - 4(1)(3) = 25 - 12 = 13
\]

Thus, the discriminant is \( \Delta = 13 \).

### Answer:
The correct option is **d. 13**.

Would you like further details or have any other questions?

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Here are 5 related questions to explore:
1. What does the discriminant tell us about the nature of the roots of a quadratic equation?
2. How does the discriminant change if the constant term is altered?
3. How can you factor a quadratic equation if the discriminant is a perfect square?
4. What is the significance of the discriminant being zero?
5. Can a quadratic equation have complex roots if the discriminant is positive?

**Tip:** The discriminant helps determine the nature of the roots—if it's positive, the equation has two real roots; if it's zero, there's one real root; and if it's negative, there are two complex roots.

Which of the following is the value of the discriminant of x^2 - 5x + 3 = 0?

Learn how to calculate the discriminant for the quadratic equation x^2 - 5x + 3 = 0. This step-by-step solution covers the key formula and concepts involved in solving quadratic equations. Suitable for students in Grades 9-10.

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