For the quadratic equation x^2 - 4x + 4 = 0, what type of roots does it have? (2
Practice Questions
Q1
For the quadratic equation x^2 - 4x + 4 = 0, what type of roots does it have? (2019)
Real and distinct
Real and equal
Complex
None of the above
Questions & Step-by-Step Solutions
For the quadratic equation x^2 - 4x + 4 = 0, what type of roots does it have? (2019)
Step 1: Identify the quadratic equation, which is x^2 - 4x + 4 = 0.
Step 2: Recognize the standard form of a quadratic equation, which is ax^2 + bx + c = 0.
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: Simplify the calculation: D = 16 - 16 = 0.
Step 7: Interpret the result: Since the discriminant D is 0, the roots are real and equal.
Quadratic Equations – Understanding the nature of roots based on the discriminant (b^2 - 4ac).
Discriminant – The value that determines the nature of the roots of a quadratic equation: positive for two distinct real roots, zero for one real root (repeated), and negative for complex roots.
