Question: The quadratic equation x^2 - 6x + 9 = 0 has how many distinct real roots?
Options:
0
1
2
Infinite
Correct Answer: 1
Solution:
The discriminant is 0, indicating that there is exactly one distinct real root.
The quadratic equation x^2 - 6x + 9 = 0 has how many distinct real roots?
Practice Questions
Q1
The quadratic equation x^2 - 6x + 9 = 0 has how many distinct real roots?
0
1
2
Infinite
Questions & Step-by-Step Solutions
The quadratic equation x^2 - 6x + 9 = 0 has how many distinct real roots?
Correct Answer: 1
Step 1: Identify the quadratic equation, which is in the form ax^2 + bx + c. Here, a = 1, b = -6, and c = 9.
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 = (-6)^2 - 4(1)(9).
Step 4: Calculate (-6)^2, which is 36.
Step 5: Calculate 4(1)(9), which is 36.
Step 6: Now, subtract the two results: D = 36 - 36 = 0.
Step 7: Interpret the discriminant: If D = 0, it means there is exactly 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.
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