For the quadratic equation x^2 - 10x + 25 = 0, what is the double root?

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Question: For the quadratic equation x^2 - 10x + 25 = 0, what is the double root?

Options:

Correct Answer: 5

Solution:

The equation can be factored as (x-5)^2 = 0, hence the double root is x = 5.

For the quadratic equation x^2 - 10x + 25 = 0, what is the double root?

For the quadratic equation x^2 - 10x + 25 = 0, what is the double root?

Step 1: Identify the quadratic equation, which is x^2 - 10x + 25 = 0.
Step 2: Look for a way to factor the equation. We want to express it in the form (x - a)(x - b) = 0.
Step 3: Notice that the equation can be rewritten as (x - 5)(x - 5) = 0.
Step 4: This means we have (x - 5)^2 = 0.
Step 5: To find the root, set (x - 5) = 0.
Step 6: Solve for x by adding 5 to both sides, which gives x = 5.
Step 7: Since the factor is squared, this root is a double root.

Quadratic Equations – Understanding the structure and solutions of quadratic equations, including factoring and identifying roots.
Double Roots – Recognizing that a double root occurs when the quadratic can be expressed as a perfect square.