If the quadratic equation x^2 + 6x + 9 = 0 is solved, what is the nature of its
Practice Questions
Q1
If the quadratic equation x^2 + 6x + 9 = 0 is solved, what is the nature of its roots? (2019)
Two distinct real roots
One real root
Two complex roots
No roots
Questions & Step-by-Step Solutions
If the quadratic equation x^2 + 6x + 9 = 0 is solved, what is the nature of its roots? (2019)
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 one real root (a repeated root).
Quadratic Equations – Understanding the standard form of a quadratic equation and how to identify its roots using the discriminant.
Discriminant – The discriminant (b^2 - 4ac) determines the nature of the roots of a quadratic equation: two distinct real roots, one repeated real root, or two complex roots.
