The quadratic equation x^2 - 4x + 4 = 0 has how many distinct real roots?

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Question: The quadratic equation x^2 - 4x + 4 = 0 has how many distinct real roots?

Options:

Correct Answer: 1

Solution:

The discriminant is 0, indicating one distinct real root.

The quadratic equation x^2 - 4x + 4 = 0 has how many distinct real roots?

The quadratic equation x^2 - 4x + 4 = 0 has how many distinct real roots?

Step 1: Identify the quadratic equation, which is in the form ax^2 + bx + c. Here, a = 1, b = -4, and c = 4.
Step 2: Calculate the discriminant using the formula D = b^2 - 4ac.
Step 3: Substitute the values of a, b, and c into the discriminant formula: D = (-4)^2 - 4(1)(4).
Step 4: Simplify the calculation: D = 16 - 16 = 0.
Step 5: Interpret the result: Since the discriminant D is 0, this means there is one distinct real root.

Quadratic Equations – Quadratic equations are polynomial equations of the form ax^2 + bx + c = 0, where a, b, and c are constants.
Discriminant – The discriminant of a quadratic equation is given by the formula D = b^2 - 4ac, which determines the nature of the roots.
Nature of Roots – The nature of the roots of a quadratic equation can be determined by the value of the discriminant: D > 0 indicates two distinct real roots, D = 0 indicates one distinct real root, and D < 0 indicates no real roots.