In the equation x^2 - 4x + 4 = 0, what is the nature of the roots? (2021)

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Question: In the equation x^2 - 4x + 4 = 0, what is the nature of the roots? (2021)

Options:

Correct Answer: Real and equal

Exam Year: 2021

Solution:

The discriminant is 0, which indicates that the roots are real and equal.

In the equation x^2 - 4x + 4 = 0, what is the nature of the roots? (2021)

In the equation x^2 - 4x + 4 = 0, what is the nature of the roots? (2021)

Step 1: Identify the equation given, which is x^2 - 4x + 4 = 0.
Step 2: Recognize that this is a quadratic equation in the form ax^2 + bx + c.
Step 3: Identify the coefficients: a = 1, b = -4, c = 4.
Step 4: Calculate the discriminant using the formula D = b^2 - 4ac.
Step 5: Substitute the values into the formula: D = (-4)^2 - 4(1)(4).
Step 6: Calculate (-4)^2, which is 16.
Step 7: Calculate 4(1)(4), which is 16.
Step 8: Now, subtract: D = 16 - 16 = 0.
Step 9: Interpret the result: Since the discriminant D is 0, it means the roots are real and equal.

Quadratic Equations – Understanding the standard form of a quadratic equation and how to analyze its roots using the discriminant.
Discriminant – The discriminant (b^2 - 4ac) determines the nature of the roots of a quadratic equation: if it's positive, there are two distinct real roots; if zero, there are two equal real roots; if negative, there are two complex roots.